Tracking Positions of Personnel, Vehicles, and Inanimate Objects

ABSTRACT

A device rotates at least one static magnetic field about an axis, producing a rotating magnetic dipole field, and is movable in relation to the surface of the ground. The field is periodically sensed using a receiver to produce a receiver output responsive to the field. A positional relationship between the receiver and the device is monitored using the output. In one aspect, changing the positional relationship, by moving the device nearer to a boring tool which supports the receiver, causes an increase in accuracy of depth determination. In another aspect, determination of an actual overhead position of the boring tool, and its application, are described. Use of a plurality of measurements over at least one-half revolution of each magnet is disclosed. Establishing a surface radial direction toward a boring tool and resolution of multi-valued parameters is described. Calibration techniques, as well as a three transmitter configuration are also described.

RELATED APPLICATION

The present application is a divisional application of co-pendingapplication Ser. No. 10/961,841, filed Oct. 7, 2004; which claimspriority from U.S. Provisional Application Ser. No. 60/510,293, filed onOct. 9, 2003; which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention is related generally to the field of positionaltracking using an electromagnetic field and, more particularly, to suchtracking using a rotating dipole field.

The prior art contains many examples of the use of an electromagneticfield for tracking and position monitoring purposes. A number of theseprior art implementations specifically utilize an electromagnetic dipolefield. In particular applications, such as, for example, horizontaldirectional drilling, a dipole field is particularly useful, at least inpart, as a result of its axisymmetric field pattern. That is, the axisof the dipole field can be oriented along the axis of a rotating boringtool in order to create a quasistatic field. It is noted that theelectromagnetic dipole field is advantageous with respect to the abilityto modulate the field with information of interest.

A more limited number of prior art implementations make use of a dipolefield wherein the dipole field axis is rotated about an axis that isgenerally perpendicular to the dipole field axis for purposes ofmonitoring position and/or orientation. Such a field can be created inthe form of an electromagnetic field by passing electrical currentthrough coils. One use of a rotating electromagnetic dipole field isdescribed by U.S. Pat. No. 3,121,228, issued to Kalmus (hereinafter the'228 patent) and entitled DIRECTION INDICATOR. This patent teaches asystem which transmits a rotating electromagnetic dipole field from aleading vehicle which is received by a following vehicle. The fieldgenerator on the leading vehicle and the receiver on the followingvehicle are each made up of a pair of orthogonal coils. The fieldgenerator is driven by an alternating current source with a 90 degreephase difference between its coils. A phase difference between thereceiver coils is used to determine orientation, while the distancebetween the receiver and generator is determined based on the sum of theinduced voltages in the receiver coils. It is of interest, however, thatthe solution which is presented assumes that the signal generator andthe receiver are coplanar with respect to one another, which istypically only the case with a level ground surface. It is consideredthat this constraint markedly narrows the usefulness of the describedmethod.

Another early prior art system is described in U.S. Pat. No. 4,812,812.Unfortunately, this system does not appear to be capable of producingdistance measurements. Further, it is submitted that the system isinoperable in the event that the transmitter is higher than thereceiver.

Another prior art implementation which uses a rotating dipole field isdescribed in U.S. Pat. No. 5,589,775 issued to Kuckes. In thisimplementation, the rotated dipole field is applied to the purpose offorming a horizontal borehole in a parallel spaced apart relationshipwith a pre-existing borehole. Formation of such a parallel borehole isuseful, for example, in steam-assisted gravity drainage (SAGD) of heavyoils. Like the '228 patent, Kuckes provides a solution in which thereceiver and field generator are assumed to be coplanar, as described incolumn 9 of the Kuckes disclosure. Any deviation from this coplanarrelationship is described as being so small as to be insignificant. Thatis, the Kuckes patent embodies the same limiting constraint that isembodied by the '228 patent by ignoring out-of-plane displacements.

U.S. Pat. Nos. 5,646,524 and 5,646,525 issued to Gilboa (hereinafter,the Gilboa patents) are directed to a targeting system for detecting theposition and orientation of a helmet using a rotating magnetic field.Unfortunately, it appears that the techniques introduced by the Gilboapatents are limited at least with respect to their use of a plurality ofdetectors that are spaced apart from one another on the helmet indetermining parameters associated with the helmet. Further difficultiesare introduced based on assumptions that the rotating magnet is fixed tothe airframe of an aircraft in a known orientation and position and thatthe helmet position is at least approximately known with respect to theairframe and, therefore, with respect to the rotating magnet. Suchconstraints may not be acceptable when the rotating magnet concept isapplied in more general tracking and locating applications.

The present invention serves to resolve the foregoing limitations andconstraints while providing still further advantages.

SUMMARY OF THE DISCLOSURE

In one aspect of the present invention, in a system including a boringtool that is movable underground using a drill string which extends fromthe boring tool to a drill rig that operates at the surface of theground, a portable device is configured for rotating a single, staticmagnetic field about an axis in a way which produces a rotating magneticdipole field and for movement in relation to the surface of the groundby an operator. At least initially, a known elevational relationship isestablished between the portable device and the boring tool. Therotating magnetic dipole field is at least periodically sensed, startingin the known elevational relationship, and a receiver is used that isprovided as part of the boring tool to at least periodically produce areceiver output responsive to the rotating dipole field. A positionalrelationship between the boring tool and the portable device ismonitored by using the receiver output to establish at least a depth ofthe boring tool such that changing the positional relationship, bymoving the portable device nearer to the boring tool, causes an increasein accuracy determination of the depth, as determined using the receiveroutput.

In another aspect of the present invention, in a system including aboring tool for underground movement in a region, a portable device isconfigured for rotating a static magnetic field about an axis in a waywhich produces a rotating magnetic dipole field emanating into theregion and for movement in relation to the boring tool by an operator atthe surface of the ground. A total signal strength of the rotatingmagnetic dipole field is sensed, at least periodically, using a sensingarrangement that is provided as part of the boring tool, to produce areceiver output responsive to a positional relationship, characterizedin three dimensions by a set of parameters, between the boring tool andthe portable device. Information is transferred, relating to thereceiver output, from the boring tool to the portable device based onthe periodically sensed total signal strength. Based on the information,at least two possible values are determined for at least a particularone of the parameters which particular parameter is multi-valued when sodetermined. The portable device is then used to provide one or moreindications that are intended to cause the operator to provide aninfluence on or to change the positional relationship based on the twopossible values. The total signal strength of the rotating magneticfield is re-sensed, responsive to the influence, for use in establishingan actual value of the particular parameter as one of the two possiblevalues.

In still another aspect of the present invention, in a system includinga boring tool for underground movement in a region, a portable device isconfigured for rotating a single static magnetic field about an axis ofrotation in a way which produces a rotating magnetic dipole fieldemanating into the region and for selective movement, in relation to theboring tool, by an operator at the surface of the ground. An initialposition of the portable device is established that is in a knownelevational relationship with the boring tool. With the portable deviceat the initial position, the rotating magnetic dipole field is sensed,using a receiving arrangement that is provided as part of the boringtool, to produce a receiver output. Information relating to the receiveroutput is transferred to an above ground location. Based on thetransferred information, at least one point of an opposing pair ofpossible overhead points on opposite sides of the portable device and onthe surface of the ground are indicated at the above ground location,where one of the possible overhead points is an actual overhead pointthat is directly above the boring tool. The portable device is movedtoward the indicated one of the possible overhead points as at least apreliminary step in establishing a direction of movement toward theactual overhead point. Thereafter, the portable device is moved in theestablished direction of movement toward the actual overhead point,while at least periodically indicating an updated position of the actualoverhead point in relation to the portable device using additionaltransferred information generated from the receiving arrangement in theboring tool.

In yet another aspect of the present invention, in a system including areceiver for underground movement in a region, a portable device isconfigured for rotating a single static magnetic field about an axis ofrotation in a way which produces a rotating magnetic dipole fieldemanating into the region and for selective movement in relation to thereceiver by an operator at the surface of the ground. An initialposition of the portable device is established that is known to be oneof vertically above or vertically below the boring tool. With theportable device above ground, a total magnetic flux responsive to therotating magnetic dipole field at the receiver is at least periodicallysensed such that the total magnetic flux is influenced by a change in arelative positional relationship between the receiver and the portabledevice, resulting from movement of at least one of the receiver and theportable device. Using the total magnetic flux, at least onecharacteristic relating to the total magnetic flux is at leastperiodically determined. The portable device is moved while monitoringthe periodically determined characteristic in a way which, at least toan approximation, establishes a surface radial direction toward anoverhead point, that is directly above the receiver, from the portabledevice.

In a continuing aspect of the present invention, in a system including aboring tool that is movable underground using a drill string whichextends from the boring tool to a drill rig that operates at the surfaceof the ground, a portable device is configured for rotating a singlestatic magnetic field about an axis in a way which produces a rotatingmagnetic dipole field and for movement in relation to the surface of theground by an operator. Starting with the portable device in a knownelevational relationship with the boring tool, a receiver, that isprovided as part of the boring tool, is used to at least periodicallysense the rotating magnetic dipole field, to produce a receiver outputresponsive to the rotating dipole field. A positional relationshipbetween the receiver and the portable device is monitored by using thereceiver output in cooperation with changing the positional relationshipto establish an actual position of an overhead point that is directlyabove the receiver in a laterally spaced-apart relationship from theportable device in a current orientation.

In a further aspect of the present invention, in a system including aboring tool that is movable underground using a drill string whichextends from the boring tool to a drill rig that operates at the surfaceof the ground, a transmitter is configured for above ground use and forrotating at least two static magnetic fields that are produced by afirst magnet and a second magnet rotating about a first axis and asecond, different axis, respectively, in a way which produces a firstrotating magnetic dipole field and a second rotating magnetic dipolefield such that the first and second rotating dipole fields aredistinguishable, one from the other. A receiver, that is provided aspart of the boring tool, is used to at least periodically sense thefirst and second rotating magnetic dipole fields, to produce a receiveroutput responsive thereto. A positional relationship between thetransmitter and the boring tool is monitored by using at least thereceiver output to establish an actual position of an overhead pointthat is directly above the receiver in a laterally spaced-apartrelationship from the transmitter.

In an additional aspect of the present invention, in a system includinga boring tool that is movable underground using a drill string whichextends from the boring tool to a drill rig that operates at the surfaceof the ground, a transmitter is configured for above ground use and forrotating at least two static magnetic fields that are produced by afirst magnet and a second magnet rotating about a first axis and asecond, different axis, respectively, in a way which produces a firstrotating magnetic dipole field and a second rotating magnetic dipolefield such that the first and second rotating dipole fields aredistinguishable, one from the other. A receiver, that is provided aspart of the boring tool, is used to at least periodically sense thefirst and second rotating magnetic dipole fields, to produce a receiveroutput responsive thereto. A positional relationship between thetransmitter and the boring tool is monitored by using at least thereceiver output to establish an actual position of an overhead pointthat is directly above the receiver in a laterally spaced-apartrelationship from the transmitter.

In another aspect of the present invention, in a system including aboring tool that is movable underground using a drill string whichextends from the boring tool to a drill rig that operates at the surfaceof the ground, a transmitter, located aboveground, is configured forrotating at least two static magnetic fields that are produced by afirst magnet and a second magnet rotating about a first axis and asecond, different axis, respectively, in a way which produces a firstrotating magnetic dipole field and a second rotating magnetic dipolefield such that the first and second rotating dipole fields aredistinguishable, one from the other. A receiver, that is provided aspart of the boring tool, is used to at least periodically sense thefirst and second rotating magnetic dipole fields, to produce a first setof receiver outputs by measuring a first plurality of total fluxintensities, in three dimensions, associated with the first rotatingmagnetic dipole as the first magnet rotates through a first plurality ofrotation angles which occur over at least one-half of a revolution ofthe first magnet such that each one of the first plurality of total fluxintensities corresponds one-for-one with each one of the first pluralityof rotation angles and to produce a second set of receiver outputs bymeasuring a second plurality of total flux intensities, in threedimensions, associated with the second rotating magnetic dipole as thesecond magnet rotates through a second plurality of rotation angleswhich occur over at least one-half of a revolution of the second magnetsuch that each one of the second plurality of total flux intensitiescorresponds one-for-one with each one of the second plurality ofrotation angles. A positional relationship between the boring tool andthe transmitter is monitored at least by using the first set of receiveroutputs and the second set of receiver outputs associated with the firstplurality of rotation angles and the second plurality of rotationangles, respectively, to establish a position of the receiver inrelation to a current position and orientation of the transmitter.

In still another aspect of the present invention, a calibrationprocedure includes positioning a transmitter, which is configured forrotating a magnet about an axis in a way which produces a rotatingmagnetic dipole field, in an at least temporarily fixed position andorientation. A receiver is arranged at a distance D from the transmitterat least approximately in a predetermined positional relationship withthe transmitter. The receiver is used to periodically sense a set oftotal flux intensities in three dimensions, of the rotating magneticdipole field, successively through a plurality of angularly distributedrotation angles of the magnet sufficient to characterize the total fluxintensity with rotation of the rotating magnetic dipole field. Using theset of total flux intensities in conjunction with distance D, a dipolestrength m of the rotating magnetic dipole field is determined.

In a further aspect of the present invention, in a system for use inlocating a receiver at a receiving position that is underground within aregion, at least a first, a second and a third transmitter are spacedapart in the region such that the transmitters produce first, second andthird rotating dipole fields, respectively, each of which fields isdistinguishable with respect to the others. A location of each of thetransmitters is established. The first, second, and third rotatingdipole fields are received at the receiving position to produce a first,a second and a third received signal. The first, second and thirdreceived signals are used to determine a first, a second and a thirdradial distance, respectively, from the receiving position to each ofthe transmitters. Using the first, second and third radial distances, inconjunction with the location of each transmitter, at least twopotential locations of the receiving position are determined in relationto the transmitters.

In an additional aspect of the present invention, in a system includinga boring tool that is movable underground using a drill string whichextends from the boring tool to a drill rig that operates at the surfaceof the ground, a transmitting device is configured for producing atleast one rotating dipole field which rotates about an axis in relationto the surface of the ground such that the transmitting device mayemanate the rotating dipole field from a tilted orientation with respectto a vertical direction. The tilted orientation is measured using a tiltsensor forming part of the transmitting device to produce a tilt signal.The rotating magnetic dipole field is sensed at a receiving position toproduce a set of flux measurements responsive to the rotating dipolefield when the transmitting device is in the tilted orientation. Usingthe set of flux measurements, a position of the receiver relative to thetransmitting device is determined in a tilted coordinate system that isdefined by the tilted orientation of the transmitting device. Theposition of the receiver is determined in a level coordinate system inrelation to the transmitting device based on the position of thereceiver, as established in the tilted coordinate system, and the tiltsignal.

In a continuing aspect of the present invention, a transmitting deviceis configured for emanating a locating signal such that the transmittingdevice may be in a tilted orientation with respect to a verticaldirection and for measuring the tilted orientation to produce a tiltsignal. The locating signal is sensed using a receiver that isunderground at a receiving position to produce one or more fluxmeasurements responsive to the locating signal when the transmittingdevice is in the tilted orientation. Using the flux measurements, thereceiving position of the receiver is determined relative to thetransmitting device in a tilted coordinate system that is defined by thetilted orientation of the transmitting device. Thereafter, the positionof the receiver is established in a level coordinate system in relationto the transmitting device, based on the position of the receiver asdefined in the tilted coordinate system in conjunction with the tiltsignal.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be understood by reference to the followingdetailed description taken in conjunction with the drawings brieflydescribed below.

FIG. 1 is a diagrammatic plan view of a magnet that is supported forrotation for use as a transmitter in accordance with the presentinvention.

FIG. 2 a diagrammatically illustrates, in elevation, a rotating magnethaving an at least generally vertically oriented axis of rotation.

FIG. 2 b diagrammatically illustrates, in elevation, a rotating magnethaving an at least generally horizontally oriented axis of rotation.

FIG. 2 c diagrammatically illustrates, in elevation, a transmitterarrangement having both generally vertically oriented and generallyhorizontally oriented rotating magnets in a side-by-side configuration.

FIG. 2 d diagrammatically illustrates, in elevation, a rotating magnetthat is rotated about two obliquely oriented axes of rotation.

FIG. 2 e diagrammatically illustrates, in elevation, a transmitterarrangement having a pair of rotating magnets in which the axes ofrotation of the respective magnets are non-normal with respect to oneanother.

FIG. 3 is a diagrammatic, perspective view of a personnel trackingsystem implemented on one floor of a building in accordance with thepresent invention.

FIG. 4 is a diagrammatic, plan view of one floor of a building in whicha personnel tracking system is implemented in accordance with presentinvention.

FIG. 5 is a diagrammatic, plan view of one floor of a building, shownhere to illustrate calibration nomenclature.

FIG. 6 a is a diagrammatic, plan view of a region in which a system fortracking an inground device such as, for example, a boring tool isimplemented using at least one transmitter having at least one rotatingmagnet.

FIG. 6 b is a diagrammatic view, in elevation, of the system of FIG. 6a.

FIG. 7 a is a diagrammatic, plan view illustrating the transmitter andreceiver of FIGS. 6 a and 6 b, shown here to illustrate further detailswith respect to the relationship between these components.

FIG. 7 b is a diagrammatic view, in elevation, illustrating thetransmitter and receiver of FIG. 7 a, shown here to illustrate stillfurther details with respect to the relationship between thesecomponents, as well as descriptive nomenclature.

FIG. 7 c is a diagrammatic view, in elevation, illustrating thetransmitter and receiver of FIG. 7 a, within the framework of anempirical tracking technique employing three regions that are arrangedaround the transmitter.

FIGS. 8 a-d are plots of magnetic field intensity versus magnet rotationangle showing how flux changes with rotation angle for typical trackingscenarios and magnet calibrations.

FIG. 9 a is a diagrammatic plan view of the rotating magnets of thetransmitter shown in FIGS. 6 a and 6 b, shown again here for purposes ofcharacterizing the relationship between these two rotating magnets.

FIG. 9 b is a diagrammatic view, in elevation, showing the rotatingmagnets of FIG. 9 a in order to illustrate further details incharacterizing the relationship between these two rotating magnets.

FIG. 9 c is a diagrammatic view, in elevation, showing nomenclature usedin determination of a rotation angle for the second one of the magnetsused in the magnet pair of FIGS. 9 a and 9 b.

FIGS. 10 a and 10 b are diagrammatic plan views illustrating a rotatingmagnet and receiver of the present invention, shown here for purposes ofdescribing calibration procedures using this system.

FIG. 11 is a diagrammatic plan view of the boring tool tracking andmonitoring system of the present invention showing one transmitter andone receiver and further illustrating a procedure for moving thetransmitter from a first position to a second position such that thetransmitter remains within range of the receiver as the receiver moves,for example, with a boring tool.

FIG. 12 is a diagrammatic plan view of a region in which a boringoperation is to be performed, shown here to illustrate the use of arotating magnet transmitter for purposes of mapping a plurality ofground surface points in this region.

FIG. 13 is an electromechanical block diagram of a transmitter or beaconincluding a rotating magnet which is rotated about a single axis ofrotation which may be used, for example, in a boring tool or personneltracker implementation.

FIG. 14 a is an electromechanical block diagram of a transmitter orbeacon including a rotating magnet which is rotated simultaneously, by asingle motor, about two orthogonal axes of rotation which may be used,for example, in a boring tool or personnel tracker implementation.

FIG. 14 b is an electromechanical block diagram of a transmitter orbeacon including a rotating magnet which is rotated simultaneously abouttwo orthogonal axes of rotation using two separate motors, one of whichis dedicated to each axis of rotation, which may be used, for example,in a boring tool or personnel tracker implementation.

FIG. 15 is an electromechanical block diagram illustrating oneembodiment of a boring tool that is configured with a receiver which isproduced in accordance with the present invention for receiving rotatingmagnet signals.

FIG. 16 is a block diagram illustrating one embodiment of a base stationwhich may be used, for example, in a boring tool or personnel trackerimplementation.

FIG. 17 is a block diagram illustrating one embodiment of a mobileposition receiver that is configured for use in a personnel trackerimplementation.

FIG. 18 a is a diagrammatic plan view, in elevation, of a portablewalkover locator, produced in accordance with the present invention,including a single rotating magnet that is arranged, for example, havingan at least generally vertically oriented axis of rotation.

FIG. 18 b is a diagrammatic view, in perspective, of the locator of FIG.18 a, shown here to illustrate its various components.

FIG. 19 is a diagrammatic view, in elevation, showing the portablewalkover locator of FIG. 18 in relation to an inground probe or receiverwhich is carried, for example, by a boring tool.

FIG. 20 is a diagrammatic plan view of the vertically oriented magnet ofthe portable walkover locator of FIG. 18 in relation to an over-the-headposition which is at the surface of the ground directly above theinground receiver of FIG. 19.

FIG. 21 is a plot of the square of magnetic field intensity versusrotation angle shown here to illustrate the way in which received fluxchanges with rotation angle of a rotating magnet.

FIG. 22 is a flow diagram illustrating one procedure for using avertical magnet locator to identify the location of the overheadposition corresponding to an associated inground receiver.

FIGS. 23 and 24 are diagrammatic views of a display which may beprovided, for example, on a single vertical magnet locator, shown hereto accompany the flow diagram of FIG. 22 in implementing the locatingprocedure when, at least initially, the boring tool may be in one of twopossible positions in relation to the locator.

FIG. 25 is a diagrammatic view, in perspective, showing a level plane aswell as a pair of tilt angles that are used to characterize tilt of themagnet with respect to this level plane.

FIG. 26 illustrates a tilted coordinate system which has undergone aroll rotation and a pitch rotation with respect to the level coordinateplane illustrated by FIG. 25 and specifically illustrating correction ofthe pitch rotation.

FIG. 27 illustrates a modified tilted coordinate system, following theroll correction and rotation of FIG. 26, and specifically illustratingcorrection of the roll rotation.

FIG. 28 is a diagrammatic plan view of a region in which a data loggingoperation is performed using the locating system of the presentinvention.

FIG. 29 is a diagrammatic view, in elevation, of the data loggingoperation of FIG. 28, illustrating further details of the region and thearrangement of the locator and probe in relation to one another.

FIG. 30 is a diagrammatic plan view of a region in which a data loggingoperation is performed using the locating system of the presentinvention wherein the locator is moved incrementally from a prioroverhead to a new or current overhead point.

FIG. 31 is a diagrammatic view, in elevation, illustrating furtherdetails with respect to the data logging operation of FIG. 30.

FIG. 32 is a diagrammatic plan view of the vertically oriented magnet ofthe portable walkover locator of FIG. 18, shown here for purposes ofillustrating an alternative angular nomenclature.

FIG. 33 is plot of minimum flux contour lines defined around an overheadpoint that is directly above an inground probe with circumferentialmovement of the locator around the overhead point.

FIG. 34 is a plot of rotating magnetic flux minimum intensity versusdistance from an associated overhead point, shown here to illustrate thesuitability of the use of minimum flux in tracking and locating theoverhead point.

FIG. 35 is a diagrammatic plan view illustrating a system including alocator having a single rotating magnet wherein the rotation axis of themagnet is at least generally horizontally arranged and showing thelocator in relation to an overhead point which is directly above aninground probe or receiver that forms another part of the system.

FIG. 36 is a diagrammatic view, in elevation, illustrating the system ofFIG. 35, shown here to illustrate further details with respect to thepositional relationship between the locator and inground receiver.

FIG. 37 is a diagrammatic perspective view of a system that uses threerotating magnets, at spaced apart locations, along with one receiver.

DETAILED DESCRIPTION

The following disclosure describes methods for tracking positions ofpeople and objects with applications in the following areas:

Tracking of Personnel and Vehicles in Buildings

-   -   An important example of this kind resides in monitoring        firefighters, police and medical aid personnel in buildings. A        suitable tracking method should have sufficient range for        accurate position monitoring across a large single story        warehouse or diagonally across several floors of a multistory        apartment or commercial building. Here, speed of equipment        deployment is of utmost importance, leaving little time for        calibration and other set-up tasks. Reliability is also an        important design consideration.    -   Tracking positions of employees in large stores will improve        customer service by more quickly dispatching needed personnel.        For this application, ease of use and system reliability is more        important than position accuracy and length of set-up time.    -   There is also much need to monitor positions of load carrying        vehicles such as forklifts in warehouses or to track robots.

Tracking of Underground Boring or Surveying Tools

-   -   The installation of underground utilities using horizontal        directional drilling requires accurate data for boring tool        position and heading directions. In this application, any        underground component of the tracking system should be small        enough to fit into standard size drill-heads and very durable to        survive the harsh operating conditions. Tracking accuracy should        be sufficient to avoid collision with underground utilities and        to stay within assigned boundaries.    -   Surveying of existing underground pipes carrying freshwater or        sewage is a related field of application.

Surveying Buildings and Outdoor Job Sites

-   -   Adopting described tracking methods to survey buildings can be a        time saving tool for interior designers since required building        dimensions can be automatically recorded and transferred to a        computer aided design program. The same mapping techniques can        also be utilized by city building departments to prepare fire        departments and police for emergency situations.    -   Similarly, the topography of outdoor job sites can be        efficiently mapped with one of the tracking methods described        below without the need for a professional surveyor.

Special Tracking Tasks

-   -   A system for monitoring positions of scuba divers, especially in        dangerous conditions such as diving under surface ice, will        serve professional rescue and construction divers as well as        recreational scuba divers.    -   The task of tracking children, club members and groups of        travelers in crowded places like amusement parks and airports        can be facilitated by a tracking system.

This disclosure includes a detailed description of two generallyapplicable embodiments of the invention. One embodiment is used fortracking personnel or movable equipment, for example, in buildings andthe other embodiment is used for determining the position of anunderground object such as, for example, a boring tool. These methodsand associated apparatus are customized for their respectiveapplications. As will be appreciated in view of the disclosure below,one of ordinary skill in the art will recognize many design options forthe main system components that can be assembled in a variety of ways tomodify the two basic embodiments and their associated methods for use inother applications.

Components of Tracking Systems

The tracking systems described in this disclosure employ four types ofcomponents called transmitter (synonyms include “beacon” and “sonde”),receiver, base-station and telemetry. Listed below are various componentdesign options enabling the user to assemble tracking systems suitablefor many different applications.

Transmitter

The function of the transmitter is to generate a three-dimensionalrotating magnetic dipole field. Transmitter design and number oftransmitters to be used depends on the intended application, trackingdistance and required position accuracy. The designer can choose from anumber of options to be described immediately hereinafter.

The dipole field can either be generated by a rotating magnet or byelectromagnetic coils. Rare earth magnets are preferred over coilssince, at low frequencies, they produce a stronger dipole field for thesame input power. Suitable magnets for this application include SamariumCobalt and Neodymium Iron Boron magnets that are usually produced in asinter process.

Throughout this disclosure, the term magnet may be used instead of themore general term transmitter, but it should be emphasized thatdescribed applications of magnets carry over to coils and wire loopswith only minor modifications.

Turning now to the figures in which like reference numbers are used torefer to like items whenever possible, it is noted that the figures arediagrammatic for purposes of enhancing the reader's understanding.Moreover, terminology such as vertical/horizontal, left/right andup/down is used for descriptive purposes only and is in no way intendedas being limiting.

Referring to FIG. 1, a magnet 10 is diagrammatically illustrated for usein the transmitter of the present invention. Each magnet to be used in atransmitter is polarized, as shown, and rotates at a constant frequency(revolutions per second) about a longitudinal axis 12. Rotationfrequencies from a fraction of 1 Hz to over 500 Hz (over 30,000 rpm) arefeasible. At distances from the magnet that are larger than its largestdimension, the field approximates that of a three-dimensional rotatingmagnetic dipole. The dipole field includes an axis of symmetry 14 whichis shown in a instantaneous position during rotation. A bearing 16supports magnet 10 for such rotation. It is noted that, throughout thefigures, the north pole of a magnet may be indicated using one or moreplus (+) signs while the south pole of a magnet may be indicated by oneor more minus (−) signs.

As will be further described, the type of motor controller used toactuate a motor that is used to rotate the magnet or magnets can varydepending on the application. There are several PID (ProportionalIntegral Derivative) type controllers that may be used, although most ofthe off-the-shelf PID controllers have many more features than arenecessary to rotate a mass at a constant rate. One such PID is availablefrom the Dr. Fritz Faulhaber GmbH, Germany, as part of a Sine WaveCommutated Servomotor with Integrated Motion Controller. In one actualimplementation, a control system uses an encoder output of the motor tomeasure its rotation frequency. A suitable microprocessor then comparesthe rotation frequency to a crystal standard and makes appropriatecorrections to the motor power. With respect to this microprocessor andall other programmable devices described in this disclosure, it isconsidered that one having ordinary skill in the art is readily capableof providing the required programming for these devices in view of thisoverall disclosure. By adjusting the frequency measuring rate and themotor power adjustment rate, the speed of the motor is kept within anacceptable range, despite differences in supply voltage, temperature andbearing changes. This type of controller is adequate for a system thatuses only radial distance to calculate a position and can readily beimplemented by one having ordinary skill in the art in view of thisdisclosure. If the phase of the transmitter (rotating magnet angle) isalso used in the position calculations, then the rotation of the magnetshould be even more precisely controlled. In particular, at lower rpm,the “compass effect” comes into play. As the motor rotates the magnet,the Earth's magnetic field will tend to increase the speed during halfthe revolution and decrease it during the other half. To overcome this,it is necessary to use a PID or other suitable controller with a motorof adequate torque to keep the rotation constant. Such an implementationcan readily be constructed by one having ordinary skill in the art inview of this description, when coupled with literature accompanyingreadily available PID's.

In the instance of using two magnets in a single transmitter enclosure,each magnet may be rotated by an independent drive mechanism such asdescribed immediately above. Alternatively, an appropriate gearbox canbe used to drive the second magnet using drive power from the drivemechanism of the first magnet. In this way, the second magnet canreadily be rotated at a different frequency than that at which the firstmagnet is rotated. It is considered that one having ordinary skill inthe art is capable of implementing such magnet rotation arrangements inview of this overall disclosure.

Turning to FIGS. 2 a-2 e, one or more rotating magnets can be packagedin different ways or configurations, each designed for a specificapplication. For example, referring in particular to FIG. 2 a, the taskof tracking receivers in a level plane can be performed with two or moretransmitter units where each transmitter unit houses a single magnet 10rotating, as indicated by an arrow 18, about a predominantly verticalaxis 20.

FIG. 2 b comprises one example in which magnet 10 rotates about an atleast generally horizontal axis 22. This embodiment is useful, forexample, in tracking an inground receiver.

Referring to FIG. 2 c, for the purpose of tracking receivers inthree-dimensional space, a single transmitter unit, generally indicatedby the reference number 30, may be used containing magnets 32 and 34with a vertical axis 36 and a horizontal axis 38 of rotation,respectively. This latter transmitter configuration may feature verticaland horizontal magnets positioned adjacent to each other, asillustrated, for example in a horizontal plane or stacked vertically(not shown). A system designed for use in three dimensions (not shown)can also consist of two or more separate transmitter units with acombination of vertical and horizontal single magnets distributed amongthe separate transmitter units. Furthermore, a magnet rotation axis neednot be limited to vertical or horizontal positions. For someapplications, orienting the magnet at other angles might improvetracking accuracy or result in more compact transmitter designs.

Referring to FIG. 2 d, a magnet 40 is shown undergoing simultaneousrotation about a first axis 42 and a second axis 44 such that the firstand second axes are at least approximately orthogonal with one another.It is noted that rotation about each of these axes produces rotation ofthe dipole axis of the magnet. Bearings and motor control of a magnetcan also be designed to spin the magnet about two axes at a differentfrequency for each axis. That is, magnet 40 can be made to spin atdifferent frequencies about the first and second axes, for example, at20 Hz about the first, longitudinal axis 42 and at 1 Hz about axis 44.Suitably chosen distinct rotation frequencies assure that the dipoleaxis sweeps a sufficiently large number of points of thethree-dimensional space surrounding the magnet. There are a number ofways available in the prior art to accomplish such dual axis rotation,as will be further described. As one example that is described infurther detail below, a magnet may be arranged for rotation by a motorabout a first axis. This motor and magnet arrangement may then bepositioned, for example, on a turntable for rotation about a second,turntable axis.

FIG. 2 e illustrates a transmitter arrangement 50 having a first magnet52 with a horizontal axis 54 of rotation and a second magnet 56 with anobliquely angled axis 58 of rotation. Such mutual orientations can berotated to any overall desired position.

In a system including multiple transmitters, each magnet of eachtransmitter can be assigned a different rotation frequency so that thetracking system is able to distinguish between transmitters on the basisof frequency.

In many applications, the position of a moving receiver is tracked whilethe transmitter is stationary. However, other types of tracking methodsare readily implemented in view of this disclosure wherein thetransmitter is mobile and receivers are stationary or where transmitterand receivers are mobile. In this regard, the present applicationenables a high degree of flexibility in describing a portable walkovertransmitter/locator for tracking a movable underground receiver house,for example, in a boring tool. Thus, both the walkover locator and theboring tool can influence the positional relationship therebetween.

A transmitter unit should be in a level position during tracking. Sinceleveling the unit manually could delay system deployment or for purposesof convenience, the transmitter unit can be equipped with a mechanism tophysically self-align. Alternatively, the transmitter unit can be fittedwith tilt sensors in order to provide compensation for magnet tilt.

Receiver

Receivers may either be stationary or attached to moving personnel,vehicles or inanimate objects whose positions are to be tracked. Theprincipal function of the receiver is to measure the components ofdipole flux from which the total flux magnitude is derived. In addition,the receiver can transfer data to and from other components of thetracking system and processes information. Design features include thefollowing.

-   -   Receivers might either transmit raw flux data or receiver        position coordinates to a base station. The computation of the        coordinates can be performed by the digital electronics in the        receiver in real-time before transmitting back to the base        station, thus saving data bandwidth on a telemetry system.    -   The flux-sensing element of a receiver may be a set of tri-axial        electromagnetic coils or a tri-axial magnetometer, e.g., of the        fluxgate type, a giant magnetoresistive sensor (GMR) or any        other suitable type sensor, either currently available or yet to        be developed. The choice of sensing element depends on many        factors including required accuracy, signal frequency, size,        weight and cost. For example, in a boring tool implementation,        it may be desirable to use a tri-axial magnetometer rather than        a coil arrangement since the latter generally requires more        space, which could adversely necessitate an increase in the        diameter of the boring tool. In an instance in which enhanced        accuracy is of concern, as opposed to available space, a larger        coil arrangement can be used. If sensor size and cost are        overriding design considerations, the receiver will most likely        feature GMR's since their high sensitivity results in the        smallest sensor size for a given receiver application and they        can be manufactured inexpensively.    -   When using magnetometers for mobile receivers, the vector sum of        the Earth's magnetic DC field can be monitored. Strong local        variations will warn the system operator of nearby ferromagnetic        material, such as steel, possibly resulting in erroneous        receiver position determinations.    -   Stationary receivers fall into two categories: Receivers used        for tracking a transmitter attached to a moving object and        receivers used for determining position and dipole strength of        stationary transmitters. The latter are used in a calibration        process to be described below.    -   In those cases where magnet dipole strength is not available        from a previous calibration in a personnel tracking        implementation, three receivers may be used to calibrate a        system for tracking in a level plane. This will facilitate rapid        deployment and eliminate any time consuming manual system        calibration. A system equipped with three such calibration        sensors/receivers can also be used to indicate the expected        placement error of rotating magnets. The mathematical        calibration technique is given below, followed by a discussion        of how to obtain magnet placement errors.    -   Each receiver must be uniquely characterized, for example, by a        unique alphanumeric identification code, if more than one moving        and/or stationary receiver is in use.

Base-Station

The function of a base-station is generally to process and displayreceiver and transmitter positions for monitoring by the systemoperator. Other types of data such as floor maps of buildings or thetopography of an outdoor job site where objects are being tracked mayalso be displayed to facilitate monitoring. In addition, thebase-station includes the capability of communicating with other systemcomponents. In some implementations, as will be self evident in view ofthe particular implementation that is being described, a base-station isnot required.

Telemetry

Telemetry enables data transmission from the receivers to the basestation and from transmitter units to receiver and/or base-station. Ofcourse, if a base station is not required, communication between thereceiver and transmitter is useful, for example, where the transmitteris a portable walkover locator for use in identifying the position of aboring tool. The combined use of telemetry and rotating magnets isheretofore unseen by Applicants and is considered to be a highlyadvantageous feature of the tracking systems and methods describedherein. In this regard, it is important to understand that a staticmagnetic field is being rotated. This static magnetic field cannot bemodulated with data of interest in the way that an electromagnetic fieldcan be modulated.

There are many small size and low-power communication transceivers thatwill meet this application requirement. In view of this overalldisclosure, those having ordinary skill in the telecommunications artsare considered as capable of designing and/or selecting from manyoff-the-shelf telecommunication sub-systems that are suitable for thisapplication.

To ensure the integrity of the data being transmitted to the basestation and generally between system components, many industry standardwireless network protocols with forward error-correction coding (FEC)can be used. The forward error-correction coding is a type of digitalsignal processing that improves data reliability by introducing a knownstructure into a data sequence prior to transmission. This structureenables a receiving system to detect and possibly correct errors causedby corruption from the channel and the receiver. This coding techniqueenables the decoder to correct errors without requesting retransmissionof the original information. Furthermore, each receiver can have adynamically assigned identification from the base station and thisidentification is used to identify the unique receiver during itsoperation. This unique identification is included in the data structurefor the communication protocol.

During normal operation, the base station displays the locations of eachof the active receivers, based on the reported coordinates andidentifications from the receivers.

A Method and System for Tracking Personnel in a Building Overview ofSystem

This embodiment of the invention is suited for monitoring a group offirefighters and/or other rescue personnel located on the same floor ofa building. Occasionally, the method will therefore be referred to as apersonnel tracker. If needed, its application can be repeated for everyfloor of a multistory building. Of course, this embodiment is readilyadaptable to tracking store personnel, people in general and inanimatemovable objects such as, for example, robots.

Referring to FIG. 3, a tracking system, produced in accordance with thepresent invention, is generally indicated by the reference number 60.Tracking system 60 and its method employs three stationary calibrationreceivers 62 a-c, two transmitter units 64 a-b, each containing a singlemagnet rotating about a vertical axis, an unlimited number of mobilepersonnel receivers 66 (only one of which is shown) and a base-station68. The transmitter and receiver are positioned, for example, on a floor69 of a building while the base station is located at a safe positionwith respect to the building. Stationary receivers 62 a-c should bepermanently installed and their position coordinates recorded before theuse of the system becomes necessary in an emergency situation. Thefunction of the three stationary calibration receivers is to rapidlycalibrate transmitters to obtain their position coordinates and dipolestrength. While the system is illustrated as being implemented on arectangular-shaped floor space with points 1-4 at its corners, it is tobe understood that this is not a requirement and that the system may beimplemented using any shape of floor space. There is no requirement thatthe calibration receivers be stationed about the periphery of thetracking space, but rather they should be sufficiently spaced apart andshould not be arranged linearly. That is, in the present example, atriangular shape of sufficient dimensions is defined by the threecalibration receiver positions in relation to the size of the trackingarea.

Nomenclature for Personnel Tracker

With reference to FIG. 4 in conjunction with FIG. 3, nomenclature usedin describing the positional relationships of the system components willnow be described. In order to further the reader's understanding,transmitters 64 a and 64 b, also labeled “magnet a” and “magnet b”,respectively, are shown in different positions in FIG. 4. It should beappreciated that this nomenclature can be modified in many ways whilecontinuing to embrace the spirit of the invention.

α=angle defined as shown in FIG. 4β=magnitude of total flux at one pointB₁,B₂,B₃=measured orthogonal components of receiver flux at one pointL=distance between magnets a & bm=magnet dipole strength of an individual magnetR=distance from center of each magnet to receiverX,Y=global two-dimensional coordinate system in a level planex,y=local two-dimensional coordinates with origin at magnet “a”

Subscripts

a=magnet “a”b=magnet “b”max=maximum flux measured by receiverr=receiver position

Measured Data

The three orthogonal components of flux B₁, B₂, B₃ induced at receiver66 by magnet “a” or “b” are measured in any convenient orthogonalcoordinate system incrementally over at least one half of a magnetrevolution, so as to create a measured set of fluxes at each rotationangle. The total flux is obtained from:

B=√{square root over (B ₁ ² +B ₂ ² +B ₃ ²)}  (1)

The maximum value of flux B_(max) can be extracted from the measured setof fluxes using standard numerical techniques. Additional details withregard to the rotation angle are given below in conjunction withdiscussions relating to the boring tool implementation of the presentinvention. It is understood, however, that these discussions are equallyapplicable with respect to the personnel tracker implementationpresently under discussion.

Knowing maximum flux, the radial distance from either magnet “a” or “b”to the receiver can be calculated using the magnetic dipole equation.

$R = \left( \frac{2m}{B_{\max}} \right)^{1/3}$

Here, m denotes dipole strength known from prior magnet calibration.

Receiver Position

FIG. 4 defines the positional relationship between movable receiver 66,magnet a and magnet b. These magnets or transmitters are assumed to bestationary for purposes of the present example. It is to be understoodthat the specific positional relationship shown in the figure is notintended as being limiting but is used only for purpose of providing anunderstanding of the defined terminology and that the illustratedrelationship represents one of an unlimited number of possiblevariations, all of which variations can be characterized using thedefined terminology. Since magnet position coordinates (X_(a),Y_(a)),(X_(b),Y_(b)) are known from transmitter calibration, receiver positioncoordinates (x_(r),y_(r)) in a local system can be calculated using thefollowing triangulation.

$\begin{matrix}{L^{2} = {\left( {X_{b} - X_{a}} \right)^{2} + \left( {Y_{b} - Y_{a}} \right)^{2}}} & (3) \\{x_{r} = \frac{L^{2} + R_{a}^{2} - R_{b}^{2}}{2L}} & (4) \\{y_{r} = {\pm \sqrt{R_{a}^{2} - x_{r}^{2}}}} & (5)\end{matrix}$

Note that the above equations contain two possible solutions for thereceiver position, from which the correct one can be chosen based onknown magnet positions. For example, placing (not shown) magnet “a” inthe corner of point 4 and magnet “b” in the corner of point 3,respectively, of the rectangular floor shown in FIG. 4 assures y_(r)>0.It is for purposes of removing this ambiguity that thetransmitters/magnets of FIG. 3 have been positioned at leastapproximately in corners.

These receiver coordinates can be transformed to global coordinatesusing

$\begin{matrix}{{\tan \; \alpha} = \frac{Y_{b} - Y_{a}}{X_{b} - X_{a}}} & (6) \\{\begin{Bmatrix}X_{r} \\Y_{r}\end{Bmatrix} = {\begin{Bmatrix}X_{a} \\Y_{a}\end{Bmatrix} + {\begin{bmatrix}{\cos \; \alpha} & {{- \sin}\; \alpha} \\{\sin \; \alpha} & {\cos \; \alpha}\end{bmatrix}\begin{Bmatrix}x_{r} \\y_{r}\end{Bmatrix}}}} & (7)\end{matrix}$

Transmitter Calibration

Transmitter calibration must be performed during deployment of thesystem, but can also be applied repeatedly during tracking. Thecalibration method assumes that position coordinates of the threestationary receivers (62 a-c) are known, given as(X_(r))_(i),(Y_(r))_(i), where (i=1, 2, 3). In addition, magnet andstationary receivers should be at about the same height above the floor.

Referring to FIG. 5, a geometric relationship is illustrated, generallyindicated by the reference number 70, between calibration receivers 62a-c and one transmitter 72 which can represent any transmitter that isused in the system. The calibration receivers are additionallydesignated in the figure as “CAL RCVR 1” through “CAL RCVR 3”. Havingrecorded the maximum fluxes induced by each magnet at the threereceivers, termed B_(max1),B_(max2),B_(max3) magnet position coordinatesare given by the following quadratic equations derived from dipoleequation (2) and the geometric relations illustrated in FIG. 5.

$\begin{matrix}{\left( \frac{B_{\max \; 2}}{B_{\max \; 1}} \right)^{2/3} = \frac{\left( {X_{r\; 1} - X_{m}} \right)^{2} + \left( {Y_{r\; 1} - Y_{m}} \right)^{2}}{\left( {X_{r\; 2} - X_{m}} \right)^{2} + \left( {Y_{r\; 2} - Y_{m}} \right)^{2}}} & (8) \\{\left( \frac{B_{\max \; 3}}{B_{\max \; 1}} \right)^{2/3} = \frac{\left( {X_{r\; 1} - X_{m}} \right)^{2} + \left( {Y_{r\; 1} - Y_{m}} \right)^{2}}{\left( {X_{r\; 3} - X_{m}} \right)^{2} + \left( {Y_{r\; 3} - Y_{m}} \right)^{2}}} & (9)\end{matrix}$

Equations (8) and (9) implicitly relate magnet position to calibrationreceiver coordinates. They can be used in a standard error analysis tofind expected errors of magnet position as functions of known receiverposition uncertainties.

Dipole strength of the rotating magnet is given by

R ₁ ²=(X _(r1) −X _(m))²+(Y _(r1) −Y _(m))²  (10)

m=0.5B_(max1)R₁ ³  (11)

The number of stationary receivers can be reduced to two and thecalibration analysis can be simplified if dipole strength is determinedindependently prior to using the tracking system. In this separatedetermination of dipole strength, the receiver is placed a knowndistance R₁ away from the magnet and the above equation for m isemployed with measured B_(max1).

Magnet position coordinates are obtained by calculating radial distancesfrom the magnet to the receivers using equation (2) and

R ₁ ²=(X _(r1) −X _(m))²+(Y _(r1) −Y _(m))²  (12)

R ₂ ²=(X _(r2) −X _(m))²+(Y _(r2) −Y _(m))²  (13)

A Method for Tracking Underground Boring Tools

Referring to FIGS. 6 a and 6 b, a boring tool tracking system isgenerally indicated by the reference number 80. FIG. 6 a illustrates aplan view of the system, while FIG. 6 b illustrates an elevational viewof the system. System 80 consists of one or more transmitter units abovea surface 82 of the ground, one of which transmitters is shown at drillbegin (transmitter 1) and one of which is shown in phantom along thedrill path (transmitter 2), a receiver 90 installed in the undergroundboring tool and base-station 68 for data communication, processing anddisplay. As seen in the plan view of FIG. 6 a, for transmitter 1, eachtransmitter unit houses two magnets termed magnets “a” and “b”. Here,the primary magnet “a” rotates about a horizontal axis and, hence, maybe referred to as a horizontal magnet whereas magnet “b” features avertical rotation axis and, hence, may be referred to as a verticalmagnet. A heavy box 92 around the magnets of transmitter 1 in FIG. 6 aindicates that the magnets are installed in the same unit together witha power supply, telemetry components, a display, keypad, CPU and motorcontroller. As mentioned, one transmitter unit is placed near the pointof drill begin where the drill head enters the ground, others arepositioned strategically along the intended drill path such that atleast one transmitter unit is always in range of the receiver.Alternatively, the user could rely on a single transmitter unit that isrepositioned during drilling. A convenient method for repositioningtransmitter units is outlined below. Each transmitter unit can beequipped with tilt sensors to avoid manual leveling. A drill path 93 isindicated as a dashed line.

Referring to FIGS. 7 a and 7 b, the former illustrates a plan view ofsystem 80 while the latter illustrates an elevational view of system 80for purposes of illustrating details with respect to the positionalrelationship between magnet “a” in transmitter 1 and receiver 90. Thesurface of the ground has not been shown since the relationship betweenthe transmitter and receiver is of specific interest. A magnetometer 94is shown as part of receiver 90. Transmitter 1 is placed on the ground,in the defined coordinate system, by orienting the axis of rotation ofthe horizontal magnet in a direction normal to a chosen initial drillingdirection 96. That is, this positioning defines a global X axis. Statedin a slightly different way, the axis of rotation of magnet “a” is alonga horizontal, global Y axis. It is to be understood, however, thatalternative coordinate system arrangements may readily be used whichrelate to the described coordinate system through translation and/orrotation. The axis of rotation of magnet “b” is arranged along a globalZ axis, as shown in the elevational view of FIG. 6 b normal to the planeof the figure. In this regard, magnets “a” and “b” may be arranged in amanner that is consistent with FIG. 2 c. It is noted that the spacingbetween the magnets results in insignificant error so long as motordrive and controller are able to overcome magnetic interactions andmaintain a sufficiently uniform magnet rotation. Any other suitablearrangement may be employed such as, for example, one where thehorizontal magnet is placed below the vertical magnet.

Receiver 90, installed in an underground boring tool (see, for anexample of such an installation, FIG. 15, described below), features acluster of three orthogonally arranged magnetometers to measure magneticfluxes emitted by transmitter 1 or 2 in three-dimensional space. Forsome applications, coils could be used instead of magnetometers.Tri-axial accelerometers (not shown) or other suitable sensors areutilized for measuring boring tool pitch and roll angles in a mannerthat is known in the art. Furthermore, the system features base-station68 for data communication, processing and display. Telemetry is thoughtto be convenient as a method for data transfer, but it is to beunderstood that data can readily be transmitted by wire up a drillstring to which the boring tool is connected, using an electromagneticsignal that is emanated directly from the boring tool or in somecombination with wireless transmission.

Each magnet should be arranged, for example, with a sensor at least toindicate the time at which its dipole axis points in a known directionand should include a suitable arrangement for communicating this toreceiver 90 such as, for example, via telemetry.

Nomenclature for Tracking Underground Boring Tools

Referring to FIGS. 7 a and 7 b, the nomenclature that is used as aframework for describing the positional relationship between eachtransmitter and the receiver will now be described. It is again notedthat the terminology that is used is not intended as being limiting andmay be modified in any suitable way.

B=magnitude of total fluxb=total flux for unit dipole strengthD=calibration distancef=flux curvefit functionh=horizontal distance between magnets “a” and “b”m=dipole strengthN=number of data sets (pointing angle, flux magnitude)P=projection of receiver position onto X,Z-planeR=distance from center of magnet to receiverr=distance from magnet to point P projected on X,Z-planet=timeX,Y,Z=global coordinate system, origin at center of magnet “a”x,y,z=rotating dipole coordinates, x-axis along dipole axisρ=rotation angleω=magnet rotation frequency

Subscripts

a=magnet “a”b=magnet “b”g=ground surfacer=receiver position

As shown in FIGS. 7 a through 7 c, the global X,Y,Z coordinate system isdefined by the placement of the rotating magnet unit (transmitter 1) onthe ground, as described above, wherein magnet “a” is specifically shownin these figures. The X,Y-axes are level and Z is upward (i.e., normalto the plane of the figure). The origin of the global coordinate systemcan be shifted to any other convenient location on the ground surfacebut the coordinates of this new origin must be recorded prior totracking.

Referring to FIG. 7 b, for each magnet, a rotating x,y,z-coordinatesystem is defined as shown, by the instantaneous position of a dipoleaxis 100 for that magnet. Note that the x-axis of the system points inthe direction of the rotating dipole axis of the horizontal magnet atall times whereas the y-axis (normal to the plane of the figure) isparallel to the axis of magnet rotation of the horizontal magnet. Theangle of magnet rotation ρ is the angle between the x-axis of thisrotating system and the global X-axis. When the dipole axis points atpoint P in the X,Z-plane the rotation angle has the value ρ_(r). It isnoted that point P is the projection of the position of receiver 90(also see FIG. 7 a) onto the X,Z-plane.

Measured Data

Receiver flux components, defined along three orthogonal axes, aremeasured at N rotation angles over at least one half of a magnetrevolution. Note that the purpose of measuring flux components is toobtain the magnitude of the total flux at the location of the receiverbased on equation (1). It is assumed that the dipole strength m of eachrotating magnet is determined by calibration as outlined below. Hence,the total flux for unit dipole strength becomes

$\begin{matrix}{b = \frac{B}{m}} & (14)\end{matrix}$

Rotation angles ρ_(i)(i=1, 2, . . . N) of the rotating dipole axis arederived from measurements of rotation frequency ω, time t₀ at which thedipole axis is horizontal (ρ=0) or at some other known rotation angleand the time t at which the dipole pointing direction is to becalculated using

ρ=ω(t−t ₀)  (15)

In order to determine the position of receiver 90 with respect to therotating magnet (RM) “a”, information regarding the rotational position(phase signal) of the RM is used. The phase or instantaneous magnetposition signal can be determined, for example, using a magnetic sensorclose to the RM or an encoder connected to the shaft of the RM. Thephase signal is transmitted to receiver 90 via a telemetry link betweenthe RM and receiver being used in an above ground application. For usein underground guidance applications, the telemetry signal can beconverted to a suitable form and sent through the drill string to and/orfrom the receiver in the drillhead. Phase signal data and measuredfluxes can be used at receiver 90, at a base station or remote, at anabove ground handheld receiver or even at the RM unit. The systemdesigner can choose a location that results in the most efficient andeconomical form of data transfer and processing. If the rotationalfrequency is suitably high, the power driving the receiver can be ACphase locked to the RM. If the rotational frequency is too low, thephase signal can be modulated onto the power line feeding the receiver.

Flux Equation

The tracking method is based on the following flux equation derived fromthe well-known magnetic dipole equations.

$\begin{matrix}{b^{2} = {{\frac{3\; r^{2}}{R^{8}}{\cos^{2}\left( {\rho_{r} - \rho} \right)}} + \frac{1}{R^{6}}}} & (16)\end{matrix}$

Here, b² is the square of the flux magnitude for unit dipole strength.The symbol R denotes the radial distance from the center of the magnetto the receiver defined by

R ² =X _(r) ² +Y _(r) ² +Z _(r) ²  (17)

The quantity r is the distance from the magnet to point P in theX,Z-plane

r ² =X _(r) ² +Z _(r) ²  (18)

FIGS. 8 a-d comprise examples of how flux changes with rotation anglefor typical tracking scenarios and magnet calibrations. The horizontalaxes of all four of these figures show rotation angles in degrees, whilethe vertical axes are representative of flux intensity.

FIG. 8 a is a first example of exact total flux induced by a rotatingdipole with a typical tracking position wherein R=100 ft and r=93.4 ft.(X_(r),Y_(r),Z_(r)=90, 25, −35.7 ft). The vertical axis shows 10¹² timesthe square of flux for unit dipole strength. This value (indicated asB²×10¹²) is plotted against rotation angle φ, as given in equation 10.An arrow 102 is used to indicate rotation angle ρ_(r).

FIG. 8 b is a second example of total flux induced by a rotating dipoledirectly overhead of the receiver wherein depth=10 ft, R=loft, and r=10ft. (X_(r),Y_(r),Z_(r)=0, 0, −10). The vertical axis shows 10⁶ times thesquare of flux for unit dipole strength. This value (indicated asB²×10⁶) is plotted against rotation angle ρ, as given in equation 10.Arrow 102 is again used to indicate rotation angle ρ_(r).

FIG. 8 c is a third example of total flux induced by a rotating dipoleshowing magnet calibration with inaccurate placement of the receiver.(X_(r),Y_(r),Z_(r)=1, 9.9, 1). The vertical axis shows 10⁶ times thesquare of flux for unit dipole strength. This value (indicated asB²×10⁶) is plotted against rotation angle ρ.

FIG. 8 d is a fourth example of total flux induced by a rotating dipole,illustrating magnet calibration with an accurate placement of thereceiver wherein D=10 ft. (X_(r),Y_(r),Z_(r)=0, 10, 0). The verticalaxis shows 10⁶ times the square of flux for unit dipole strength. Thisvalue (indicated as B²×10⁶) is plotted against rotation angle ρ.

Receiver Position Coordinates

Turning to FIGS. 9 a-c, magnet “a” and magnet “b” are diagrammaticallyillustrated in relation to the global or overall coordinate system. Inthis regard, the above equations are now applied to analyze fluxesinduced by magnets “a” and “b” to obtain the receiver position in globalcoordinates. Notice that magnet “a” coordinates X_(a),Y_(a),Z_(a) areidentical with global X,Y,Z-coordinates but magnet “b” coordinates aredefined differently, as seen below. The analysis begins by processingmagnet “a” fluxes.

Equation (16) suggests the following curvefit of the measured fluxes

f=c ₁ cos²(c ₃−ρ)+c ₂  (19)

Comparing flux equation (16) and curvefit (19) yields the followingformulas for the radii R,r.

$\begin{matrix}{R^{2} = \left( \frac{1}{c_{2}} \right)^{1/3}} & (20) \\{r^{2} = \frac{c_{1}R^{8}}{3}} & (21)\end{matrix}$

In order to calculate rotation angle ρ_(r) from coefficient c₃, it isnoted that two possible values of this coefficient exist: c₃ and c₃+π.Therefore, two solutions for angle ρ_(r) (see FIG. 7 b) are given as:

ρ_(r)=c₃  (22)

ρ_(r) =c ₃+π  (23)

The correct value can be determined, for example, by employing anempirical technique which is similar to the one disclosed in U.S. Pat.No. 6,727,704, entitled BORING TOOL TRACKING/GUIDING SYSTEM AND METHODWITH UNCONSTRAINED TARGET LOCATION GEOMETRY (hereinafter the '704patent) which is commonly owned with the present invention andincorporated herein by reference. It is most often the case that thedrillpath is below the elevation of the magnet with a generally levelground surface. In this case, the value of ρ_(r) is selected to placethe receiver relatively lower than the rotating magnets. FIG. 7 crepeats the framework shown in FIG. 6 of the '704 patent whichillustrates magnet “a” and receiver P in an elevational view. Forpurposes of the present, simplified discussion, the ground around magnet“a” is divided into three regions that are designated as A, B and C. TheX,Z-coordinate system includes the rotating magnet at its origin. Inmost drilling scenarios, the receiver within the boring tool travelsbelow the magnet(s) along a path nearly parallel to the X-axis. Thehalf-width h of region B is chosen such that it is much larger than thedistance traveled by the underground receiver between two consecutivepositions at which data are recorded. For many applications, a value forh of 15 feet is an appropriate choice. Magnet position and region B mustbe chosen such that, in this region, the drillpath is either entirelybelow or above the magnet. The user notifies the tracking system whetherthe drillpath is above or below the magnet in region B. Table 1 definesregions A, B, C in terms of the receiver P position X-coordinate,denoted by the symbol X_(r).

TABLE 1 Region X_(r)-coordinate A −∞ < X_(r) < −h B −h ≦ X_(r) ≦ h C   h< X_(r) < ∞

In each region of regions A-C, rotation angle ρ_(r) is uniquely definedby limiting the possible receiver positions to two quadrants, as seen inTable 2. Drilling can begin in any of the regions defined by Table 1 andproceeds such that the distance between two consecutive data readings isalways less than the half-width of region B. Therefore, tracking thedrillhead receiver from region A or from the left part of region B to Cwill always yield some position data in region B and clearly definesrotation angle ρ_(r) when the receiver crosses the boundary betweenregions B and C.

TABLE 2 Region Receiver coordinate X_(r) Rotation angle ρ_(r) A −∞ <X_(r) < −h  90° ≦ ρ_(r) ≦ 270° B −h ≦ X_(r) ≦ h  0° ≦ ρ_(r) ≦ 180°drillpath above magnet −h ≦ X_(r) ≦ h 180° ≦ ρ_(r) ≦ 360° drillpathbelow magnet C   2h < X_(r) < ∞ −90° ≦ ρ_(r) ≦ 90°

Referring to the notation illustrated in FIGS. 7 a-b and equations (17)and (18), receiver position coordinates are obtained from

X_(r)=r cos ρ_(r)  (24)

Z_(r)=r sin ρ_(r)  (25)

Y _(r) =±√{square root over (R ² −r ²)}  (26)

As seen in the last equation, there is not sufficient informationavailable from measurements of fluxes of magnet “a” to decide if thereceiver is to the right or left of the transmitter unit. However, whenflux data emitted by magnet “b” are taken into account, the correctlateral position can be determined, as will be shown immediatelyhereinafter.

As shown in FIGS. 9 a and 9 b, in the present example, magnet “b” isinstalled adjacent to the primary magnet “a”. A horizontal offsetbetween the two magnets is labeled h. Both magnets rotate at differentfrequencies (e.g., 7 and 11 Hz) so that their respective signals can bedistinguished by the receiving magnetometers. FIGS. 9 a-c illustrate thefollowing relations between the coordinates of magnets “a” and “b”:

X _(a) =X _(b) +h  (27)

Y_(a)=Z_(b)  (28)

Z _(a) =−Y _(b)  (29)

Fluxes of magnet “b” are measured as a function of magnet “b” rotationangle, similar to the data acquisition of magnet “a”. They arecurvefitted as described above for magnet “a” in order to obtain r_(b),R_(b) defined as the radii from the center of magnet “b” to point P_(b)in the X_(b),Z_(b)-plane and the receiver, respectively, as shown inFIG. 9 c. The radii r_(b),R_(b) are expressed in terms of receivercoordinates by

R _(b) ² =X _(b) ² +Y _(b) ² +Z _(b) ²  (30)

r _(b) ² =X _(b) ² +Z _(b) ²  (30)

However, the determination of rotation angle ρ_(r) _(b) (see FIG. 9 c)of magnet “b” is different from that of magnet “a”. Since theX_(a)-coordinate of the receiver is already known from the magnet “a”analysis, ρ_(r) _(b) follows from

$\begin{matrix}{{\cos \; \rho_{r_{b}}} = \frac{X_{a} - h}{r_{b}}} & (32)\end{matrix}$

Finally, the Y_(a)-coordinate of the receiver in the global system isgiven by

Z_(b)=r_(b) sin ρ_(r) _(b)   (33)

Y_(a)=Z_(b)  (34)

Notice that the main purpose of adding a second magnet to the trackingsystem is to determine the left/right position of the receiver. Inaddition, the second magnet provides redundant data that may be utilizedto monitor data acquisition and processing.

Calibration of Rotating Magnet

Referring to FIGS. 10 a and 10 b, a calibration arrangement is shown inplan view for calibration of a rotating magnet system and is generallyindicated by the reference number 120. A rotating magnet 122 isdiagrammatically shown along with a receiver 124. The dipole field axisis indicated by reference number 126. FIG. 10 a illustrates receiver 124at a distance “D” from the magnet along its axis of rotation (i.e., theY axis). FIG. 10 b illustrates receiver 124 at a distance “D” from themagnet along the X axis. As will be seen, either of these spatialconfigurations can be used for calibration. It is noted that thisprocedure is similar to a one-point transmitter calibration used inwalkover locating systems. Each magnet of a tracking system, employingtwo or more magnets, must be calibrated separately. The calibration canbe conducted by placing the rotating magnet on the ground (not shown),with its axis of rotation leveled, as shown. Receiver 124 is then placedon the axis of magnet rotation a distance D (e.g., 10 ft) to the side ofthe magnet, as shown in FIG. 10 a. Alternatively, the receiver may beplaced on the global X-axis as seen in FIG. 10 b. Note that the receivermay be positioned at any angle with respect to the magnet rotation axisor the X-axis. Referring to FIG. 10 a, calibration includes placing thereceiver on the magnet rotation axis, for example, and measuring themagnitude of total flux as described above for a large number ofrotation angles. Generally, twelve angles is sufficient, however, theuse of more angles equates with further enhancement of accuracy. Anaverage flux B_(av) is used to determine dipole strength m from

m=D³B_(av)  (35)

It is of interest that, for perfect receiver positioning, relative tothe transmitter, during calibration, only one measurement is required.Multiple measurements effectively accommodate receiver positioningerrors when used to determine an average flux. Magnet calibration withthe receiver on the global X-axis, as shown in FIG. 10 b, uses slightlydifferent formulas to obtain dipole strength. This is due to thevariation of flux magnitude, showing distinct flux minima and maxima,labeled B_(min), B_(max), over one magnet revolution. Specifically,dipole strength is determined in this configuration using

m=D³B_(min)  (36)

m=0.5D³B_(max)  (37)

Relocation of Transmitter Unit

Turning to FIG. 11, transmitter relocation is generally illustrated in aplan view, as indicated by the reference number 130. Accordingly,transmitter 1 (T1) is to be relocated relative to a receiver 134 from aposition 1 (P1) to a position 2 (P2). Such relocation of the transmitterbecomes necessary when the receiver approaches the range limit foraccurate flux measurements. It is noted that the plane of the figurerepresents the global X,Y plane with Z being normal thereto. Thefollowing procedure applies.

Receiver 134 coordinates X_(1r),Y_(1r),Z_(1r) are recorded with thetransmitter in one position, as shown. The receiver is kept in thislocation until the transmitter relocation is completed.

Still referring to FIG. 11, the transmitter is moved to position 2 whereit either may be placed with its X₂-axis pointing in the same directionas X₁ (shown as X₂′, along with Y₂′) or the transmitter may be rotatedby Δβ. Any change of heading angle must be measured in a suitablemanner.

The receiver coordinates X_(2r),Y_(2r),Z_(2r) are recorded with thetransmitter in position 2 (P2).

If X₂ is not aligned with X₁, receiver coordinates must be rotated tothe X₂′,Y₂′,Z₂′-system using

$\begin{matrix}{\begin{Bmatrix}X_{2\; r}^{\prime} \\Y_{2\; r}^{\prime} \\Z_{2\; r}^{\prime}\end{Bmatrix} = {\begin{bmatrix}{\cos \; \Delta \; \beta} & {{- \sin}\; \Delta \; \beta} & 0 \\{\sin \; \Delta \; \beta} & {\cos \; \Delta \; \beta} & 0 \\0 & 0 & 1\end{bmatrix}\begin{Bmatrix}X_{2\; r} \\Y_{2\; r} \\Z_{2\; r}\end{Bmatrix}}} & (38)\end{matrix}$

The translation of transmitter position follows from

ΔX=X _(1r) −X _(2r)′  (39)

ΔY=Y _(1r) −Y _(2r)′  (40)

ΔZ=Z _(1r) −Z _(2r)′  (41)

Subsequent tracking of the receiver may be conducted in the X₂,Y₂,Z₂system. If necessary, coordinates are rotated to the X₂′,Y₂′,Z₂′-systemusing equation (38). Transformation to the X₁,Y₁,Z₁-coordinate systemutilizes ΔX,ΔY,ΔZ obtained during relocation of the transmitter.

Depth Measurement

Continuing to refer to FIG. 11, the rotating magnet provides fordetermination of the vertical position of receiver 134, Z_(r), that isgenerally not the same as depth, depending upon the topology of theground. Since depth is defined as the vertical distance from the groundsurface to the drill path, ground topography can be mapped in order toobtain depth. For this purpose, the rotating magnet methodologydescribed above can be used without modification. Prior to drill begin,the magnet is placed on the ground and the receiver or another devicecontaining a cluster of tri-axial magnetometers is placed at a number ofpoints on the ground that is sufficient to determine the surfacecoordinates, as will be described with reference to FIG. 12. The lattercan either be recorded by pausing at each surface point, taking discretemeasurements or by acquiring streaming data continuously.

Turning to FIG. 12, ground surface 82 is shown referenced to the overallX,Y coordinate axes in a plan view, along with transmitter T1. Usingeither discrete or continuous measurements, ground surface 82 is mappedat a large number of points 140, one of which is labeledX_(g),Y_(g),Z_(g). The points can be recorded in any convenient orderand with unequal spacing, as shown. Notice that only a few points areneeded to define a nearly level ground, whereas much denser pointspacing is generally required for rapidly sloping surfaces. The rotatingmagnet can be moved, using the same procedure described above fortracking, to extend the range.

During drilling beneath the exemplary surface of FIG. 12, receivercoordinates X_(r),Y_(r),Z_(r) (FIG. 11) are determined as discussedpreviously. Since the X_(r),Y_(r)-coordinates will usually fall betweenthe measured ground surface points X_(g), T_(g), the ground elevation Z_(g) above the actual receiver position should be determined byinterpolation. Standard methods such as the interpolation of scattereddata based on Delaunay triangulation are available in the openliterature to accomplish this efficiently. The desired receiver depthbecomes simply the difference Z _(g)−Z_(r).

FIG. 13 is an electromechanical block diagram illustrating oneembodiment of a transmitter or beacon which is produced in accordancewith the present invention and generally indicated by the referencenumber 150. The latter includes a magnet 152 that is connected to amotor shaft 154 and motor 156 for rotation thereby. Motor shaft 154 is,in turn, connected to an encoder 158. A motor controller 160 which maybe a PID or other suitable controller, in view of a particularapplication, receives the encoder signals on a line 162 and providesdrive signals to the motor via a line 164. Additionally, the encoderinformation can be used to determine instantaneous magnet position inapplications where the phase of the rotating magnet is necessary. A CPU170 is interfaced with an input device such as a keypad 172 and providesoverall control to the motor controller, a display 174 and a telemetrytransceiver 176. The display may provide information including, but notlimited to diagnostics, information about user data input which, forexample, may assign a beacon number and telemetry parameters. Telemetrytransceiver 176 is used for a number of purposes including, but notlimited to communication with other beacons, base stations and mobileposition receivers, shown in subsequent figures. The type of informationcommunicated can include, but is not limited to instantaneous rotationalposition of magnet 152, magnet position synchronization signals,diagnostic and control information. A power supply section 180distributes power, as needed, throughout the beacon.

FIG. 14 a is an electromechanical block diagram illustrating oneembodiment of a dual axis beacon that is produced in accordance with thepresent invention and generally indicated by the reference number 200.In this embodiment, a drive motor 202 includes an output shaft 204 whichdirectly spins magnet 152 as well as an x encoder 206. The motor furtherdrives a gearbox 208 having a gearbox output shaft 210 which is used torotate a turntable 212 using a pinion gear 214 positioned against afixed gear 216. The turntable supports motor 202, magnet 152 and xencoder 206 for rotation thereon. Motor 202 is electrically driven by amotor controller 218 responsive to CPU 170. It should be appreciatedthat x encoder 206, motor 202, magnet 152, gearbox 202 and pinion gear214 all rotate with turntable 212. Motor drive and x encoder signals arepassed through a turntable shaft commutator 222. Turntable shaft 224also drives a y encoder 226 having an output 228 that is provided to CPU170. The latter also operates telemetry transceiver 176 and display 174while receiving user inputs from an input device such as keypad 172.Power supply section 180 provides electrical power to the variouscomponents, as needed.

FIG. 14 b is an electromechanical block diagram illustrating anotherembodiment of a dual axis beacon that is produced in accordance with thepresent invention and generally indicated by the reference number 250.In this embodiment, a first, x drive motor 252 includes an output shaft254 which directly spins magnet 152 as well as x encoder 206, all ofwhich is mounted on a turntable. A second, y motor 256 drives aturntable 258 which is supported for rotation at a center of rotation260 in a suitable manner. Motors 252 and 256 are electrically driven byrespective x and y motor controllers, indicated by the reference numbers218 and 264, responsive to CPU 170. Motor drive and x encoder signalsare passed through turntable shaft commutator from x motor controller218. Turntable shaft 224 also drives a y encoder 268 having an output270 that is provided to CPU 170 for use in driving a y motor controller272. The latter also operates telemetry transceiver 176 and display 174while receiving user inputs from an input device such as keypad 172. Allof x encoder 206, x motor 252 and magnet 254 rotate with turntable 258.Power supply section 180 provides electrical power to the variouscomponents, as needed. It should be appreciated that any number ofalternative structures can be provided for purposes of implementing dualaxis rotation of a magnet and that the present descriptions are notlimited to the described embodiments.

FIG. 15 is an electromechanical block diagram illustrating oneembodiment of a boring tool that is configured in accordance with thepresent invention and generally indicated by the reference number 280.Boring tool 280 includes a slotted non-magnetic drill tool housing 282.A triaxial magnetic field sensing arrangement 284 is positioned inhousing 282. For this purpose, a triaxial magnetometer or coilarrangement may be used depending on considerations such as, forexample, space and accuracy. A triaxial accelerometer 286 is alsolocated in the housing. Outputs from magnetic field sensing arrangement284 and accelerometer 286 are provided to a processing section 288having a microprocessor. A dipole antenna and associated transmitter 290are located in the boring tool which can be used, responsive to theprocessing section, for telemetry purposes, for transferring encodeddata such as roll, pitch, magnetometer readings and accelerometerreadings to above ground locations and for locating determinations suchas, for example, determining a distance to the boring tool. Generally,the dipole axis of the dipole antenna is oriented coaxially with anelongation axis of the boring tool in a manner which is well-known inthe art. Of course, all of these functions are readily supported by theprocessing section which reads appropriate inputs from the magnetometerand accelerometer, performs any necessary processing and then performsthe actual encoding of information that is to be transmitted.

Still referring to FIG. 15, a regulated power supply 292, which may bepowered using batteries, is provided for providing appropriate power toall of the components in the boring tool, as shown. It is noted thatmagnetic field sensor 284 can be used to measure the field generated bya rotating magnet as well as measuring the Earth's magnetic field. Thelater may be thought of as a constant, much like a DC component of anelectrical signal. In this instance, the Earth's magnetic field may beused advantageously to determine a yaw heading. Further, the magneticfield sensor can be used to pick up magnetic fields that are of interestand which are generated by other sources, for example a signal that isgenerated by a buried line for purposes of collision avoidance. As analternative to sending information above ground from the dipole antenna,a wire-in-pipe approach may be used wherein a conductor in a drillstring, which moves the boring tool, transfers the information aboveground as described, for example, in commonly owned U.S. Pat. No.6,223,826 entitled AUTO-EXTENDING/RETRACTING ELECTRICALLY ISOLATEDCONDUCTORS IN A SEGMENTED DRILL STRING, which is incorporated byreference in its entirety. It is noted that this approach may also beused to provide power to power supply 292 from above ground, as analternative or supplemental to the use of batteries.

FIG. 16 is a block diagram illustrating one embodiment of a base stationthat is configured in accordance with the present invention andgenerally indicated by the reference number 300. It is noted that theillustrated configuration is generally applicable to both the personneltracker and boring tool implementations of the present invention. Ofcourse, display sizes and specific display information is readilychanged to best suit each application. Base station 300 includes atelemetry transceiver section 302 that is in electrical communicationwith a processing section (CPU) 304. The processing section utilizes adata storage section 306 which may comprise any suitable form of digitaldata storage including but not limited to ROM, RAM and hard disks.Further, processing section 304 generates drive signals for a display308. Any suitable display may be utilized including, but not limited toLCD, LED and plasma displays. An input device such as, for example, akeypad or keyboard 310 is interfaced with the processing arrangement inorder to provide for user input. A power supply 312 provides power tobase station components, as illustrated. In the personnel trackingimplementation, the base station may receive “raw” data throughtelemetry signals 314 from one or more portable position receivers. Thatis, signals received by a position receiver may be passed to the basestation, as compared to the position receiver actually determining itsposition. The base station uses the raw data to determine the positionof an associated one of the receivers. Alternatively, the base stationmay be sent receiver determined position coordinates.

FIG. 17 is a block diagram illustrating one embodiment of a mobileposition receiver (MPR) that is configured in accordance with thepresent invention and generally indicated by the reference number 320.The MPR includes a triaxial magnetic field sensor 322 such as, forexample, triaxial magnetometers or coils (if space permits). The fieldsensor is interfaced with a hardware filter 324 which removesfrequencies that are higher than the magnet frequency, including 50/60cycle noise. In the present example, a low pass filter is used, asdepicted in the figure. Additional filtering may be performed by aprocessing section 326, interfaced with the filter, to provide fornarrow, bandpass capability that can be centered on a specific magnetfrequency of interest. Of course, frequencies associated with differentmagnets can be discriminated in this way. The processing section is alsointerfaced with a telemetry transceiver 328 and a suitable display 330.The latter can be used to show a display which is similar to that of abase station such as, for example, base station 300 of FIG. 16, withwhich it is in communication. For example, MPR 320 can show its owndetermined location. It is noted that display 330 is optional. In thecase where a display is provided, data entry device 310 can be provided.A power section 332 provides power to the various components, asnecessary, and may be configured for battery operation. As noted above,the MPR may be configured to send raw data to an associated base stationusing telemetry transceiver 328. Alternatively, the MPR may beconfigured to determine its actual location. In this instance, the MPRmust have available to it beacon positions in absolute coordinates. Thisinformation can be provided, for example, via telemetry.

Having described a dual magnet boring tool tracking/monitoring system indetail above with reference to the foregoing figures, a description ofsuch a system will now be provided which uses a single rotating magnet.To that end, attention is immediately directed to FIGS. 18 a and 18 b,which illustrate a portable walkover locator produced in accordance withthe present invention and generally indicated by the reference number400. Locator 400 is configured with a handle 402 for hand-carried use,shown in a diagrammatic plan view in FIG. 18 a and in a diagrammaticperspective view in FIG. 18 b.

Referring to FIG. 18 a, locator 400 houses a single magnet 404 that canrotate slowly, for example, at about 20 revolutions per second (20 Hz),as indicated by an arrow 405 thereby emitting a rotating magnetic dipolefield 406 (only partially shown) having a dipole axis 408. It is notedthat the rotational axis of magnet 404 is coaxial with an overall Z axisand is centered in an X,Y plane of this coordinate system which moveswith locator 400. With locator 400 held in a level orientation, X and Yare in the plane of the figure and Z is normal thereto.

FIG. 18 b diagrammatically illustrates further details with respect tothe components which make up locator 400. In particular, a dataprocessing and control or CPU section 404 is provided and interfacedappropriately with other described components in a known way. Theseinterface connections have not been illustrated for purposes ofillustrative clarity at least for the reason that configuring such anarrangement is considered to be within the capability of one havingordinary skill in the art. Additional components include a telemetrysection 406 that is interfaced with a telemetry antenna 407. A signalacquisition section 408 serves to amplify and digitize the signal frommulti-axis dipole antenna 409 before passing it to the CPU. The magneticflux components from the rotating magnets measured by the sensors aredigitized and encoded before being transmitted by a dipole antenna orwire-line. The multi-axis dipole antenna in handheld receiver 409 isused to measure the underground dipole antenna's flux components. TheCPU extracts the encoded digital signal that contains the measuredmagnetic flux components emitted by the rotating magnet. User inputs areprovided by a suitable device such as, for example, a keypad 410, whileinformation can be displayed to the user on a display 411. An audiooutput device 412 may be used to provide audio indications such as, forexample, alarms and to indicate actuation of the various keys which makeup keypad 410. Keypad 410, display 411 and audio device 412 are operatedusing an interface 413. A motor 414 rotationally drives magnet 404 andan encoder 415, suitably supported for rotation using a bearingarrangement 416.

Referring to FIG. 19 in conjunction with FIGS. 18 a and 18 b, locator400 is part of a tracking system, generally indicated by the referencenumber 420, that also includes a receiver 422 that is installed in anunderground probe such as, for example, a steering tool or boring tool(see FIG. 15). Fluxes are measured at the probe by tri-axialmagnetometers or coils 284. FIG. 19 is an elevational view showing probe422 beneath ground surface 82. It should be appreciated that this highlyadvantageous system improves drillhead tracking, over prior art systems,for a number of reasons to be described immediately hereinafter.

-   -   This should provide accurate tracking under rebar (i.e., steel        concrete reinforcement bar) due to the very low frequency of the        rotating dipole field. It is considered that a frequency of        approximately 20 Hz is orders of magnitudes below the        frequencies at which present-day locating systems operate. For        example, current systems produced by Digital Control, Inc.        operate at a low frequency of approximately 1.5 kHz. For this        reason, rebar effects should be dramatically reduced.    -   An improved locating capability is provided since actual probe        position relative to the locator can be determined and        displayed. The locating procedure focuses on finding an        over-the-head position 430 on ground surface 82 immediately        above probe 422. For this purpose, the new locator uses a highly        intuitive “ball-in-the-box” display, however, the “ball” is a        representation of the actual over-the-head coordinates, a        technique which has never heretofore been available to        Applicant's knowledge.

The following disclosure describes three different types of rotatingmagnet locators, of which two utilize a single magnet having a verticalrotation axis, and the third employs a single horizontal magnet. Otherembodiments can be designed featuring a single magnet with an obliquerotation axis. A multiple magnet embodiment is described above. Dataacquisition and analysis, locating procedure, tilt corrections and otherdesign features of the vertical magnet locator described below areapplicable to all of these rotating magnet locators with only minormodifications.

Vertical Magnet Locator

Referring again to FIGS. 18 a, 18 b and 19, locator 400, as will now beappreciated, comprises a vertical magnet embodiment. Nomenclature usedin characterizing system 420 is described immediately hereinafter. It isnoted that this nomenclature is in no way intended as limiting and maybe modified in any number of suitable ways by one having ordinary skillin the art in view of this overall disclosure.

Nomenclature

-   b=total flux at probe for unit dipole strength-   f=flux curvefit function-   OH=over-the-head position-   p=probe-   R=total distance from center of magnet to flux sensor-   r=horizontal distance from magnet to over-the-head position-   t=time-   X,Y,Z=leveled locator coordinate system, origin at center of magnet,    X-axis in plane of locator symmetry, X,Y-axes are level-   X′,Y′,Z′=tilted locator coordinate system, origin at center of    magnet, X-axis in plane of locator symmetry-   x,y,z=rotating dipole coordinates, x-axis along dipole axis, z-axis    along vertical magnet rotation axis-   Z_(p)=vertical distance between locator and probe, depth of probe    below a level ground-   ρ=rotation angle-   γ_(x),γ_(y)=tilt-pitch and tilt-roll angles-   λ,θ0=Euler pitch and roll angles-   ω=magnet rotation frequency

The symbol r defines the horizontal distance from magnet 404 to aprojection of the over-the-head location onto a level plane that passesthrough the magnet (FIG. 19), whereas R denotes the total distance fromthe magnet to the probe. True depth of the probe, defined as thevertical distance between ground and probe, is usually different fromdepth Z_(p), but becomes equal when the locator is over-the-head(normally including some distance above the actual surface of the groundat which the locator is held). It is noted that FIG. 19 illustrates asituation in which Z_(p) is less than the actual depth since overheadpoint 430 is vertically higher than overhead point 430.

Referring to FIG. 20, a diagrammatic plan view of system 420 isprovided, showing overhead point 430 with probe 422 (FIG. 19)therebeneath. A rotation angle ρ is defined in a horizontal plane of thefigure, measured from the X-axis of the locator coordinate system todipole axis 408. Angle ρ has the value ρ_(OH) when the dipole axispoints or aligns in the direction of the over-the-head position. In thisaligned condition, maximum flux is present at the probe, with minimumflux present when the dipole axis is normal to a line which extendsbetween the locator and the over-the-head position.

Measured Data

Flux magnitude b for unit dipole strength is measured. Note that magnetcalibration is required to determine dipole strength before using thelocator. Rotating magnet calibration methods are discussed in detailabove.

Magnet rotation angles ρ for at least half of a magnet revolution aremeasured, with corresponding total flux magnitudes at these angles. Theminimum number of required rotation angles depends on desired curve-fitaccuracy. Accurate curve-fits can often be achieved with 12 angles orfewer, but modern data acquisition and processing techniques readilypermit use of much larger data sets consisting of several hundredangles.

It is noted that walkover locators, as described herein, do not requireknowledge of the locator position itself, since only the relativeposition between locator and probe or receiver is of interest. However,some users might want to log drillhead position data in an Earth fixedcoordinate system that would require measurement of locator position.Methods for logging probe positions are discussed at an appropriatepoint below.

Data Analysis

The data analysis proposed for the locator of the present invention maybe referred to as a “phase method”, described above, but is summarizedhere for easy reference and with modifications suiting the nomenclatureof a single vertical magnet system.

A flux b induced by the magnet at the probe varies according to

$\begin{matrix}{b^{2} = {{\frac{3\; r^{2}}{R^{8}}{\cos^{2}\left( {\rho_{OH} - \rho} \right)}} + \frac{1}{R^{6}}}} & (42)\end{matrix}$

Referring to FIG. 21, a plot 440 is presented showing the square of theflux magnitude for unit dipole strength b² multiplied by 10¹², along thevertical axis of the figure plotted against ρ, illustrating how fluxchanges with rotation angle according to equation (42). Flux plot 440exhibits a b_(max) ² value 442 and a b_(min) ² value 444. Hence, asuitable curvefit for measured square fluxes can be written as

f=c ₁ cos²(c ₃−ρ)+c ₂  (43)

Equations (20) and (21), for R and r, described above, are againobtained by comparing equations (42) and (43).

In order to determine rotation angle ρ_(OH) from coefficient c₃, it isnoticed that two possible values of this coefficient exist, c₃ and c₃+π.Therefore, the following two solutions for rotation angle are obtained

ρ_(OH) ₁ =c ₃  (44)

ρ_(OH) ₂ =c ₃+π  (45)

With reference to FIG. 20, probe position coordinates can be determinedusing

X _(p) =r cos(ρ_(OH))  (46)

Y _(p) =r sin(ρ_(OH))  (47)

Z _(p) =±√{square root over (R ² −r ²)}  (48)

Equations (45)-(48) reveal ambiguities in calculating probe positionthat are due to multiple values for rotation angle and probe depth. Thevalid solutions for over-the-head position X_(p),Y_(p) and depth Z_(p)can be determined by applying the locating procedure outlined below in aconsistent manner.

Locating Procedure

Referring to FIG. 19, this procedure focuses on finding theover-the-head position for which coordinates X_(p),Y_(p) are determinedas described above. Over-the-head position is displayed, for example, ona suitable display, as will be shown in FIGS. 23 and 24, using anintuitive, “ball-in-the-box” display, as described in more detail below.It is important to understand, however, that this new procedure isthought to be fundamentally different from any prior techniques, atleast for the reason that the actual over-the-head position, defined byits coordinates X_(p),Y_(p), is displayed relative to the locator. Thatis, flux line curvature does not cause the displayed location to becomean approximated location of the over-the-head point. In the past, suchan approximated positional display was used to find a forward or rearlocate point as described in U.S. Pat. No. 6,496,008 which isincorporated herein by reference and is commonly owned with the presentapplication. At the time of its discovery, the “ball-in-the-box” displayof an approximated locate point position represented a sweepingimprovement over the then-existing state-of-the-art, and served as anaid in displaying further, more accurate positions of the locate pointwith subsequent movement of the locator. Further, this approach remainsin use at the time of this writing. Here, however, the “ball” representsthe location of the over-the-head position in actual coordinatesrelative to the locator. In some circumstances, this feature isparticularly advantageous such as, for example, when the operator isunable to move the locator closer to the over-the-head point due to anobstacle such as a building. The present approach remains equallyintuitive wherein the operator moves the locator while observing thedisplay and adjusts this movement to move the “ball” toward and into the“box.”

Referring to FIG. 22 in combination with FIGS. 18 a and 19, the locatingprocedure is generally indicated by the reference number 460 and beginswith step 462 for establishing a vertical positional relationshipbetween probe 422 and transmitter magnet 404. In other words, therelationship is limited to specifying whether the locator is above orbelow a level plane that extends through the probe, characterized as adirection of vertical offset of the locator with respect to the probe.With specific reference to FIG. 19, it should be appreciated that in amajority of cases, this relationship is readily ascertainable, if notalready known, by the operator. Moreover, for directional drilling thehandheld locator is most often vertically higher than the receiver inthe drill-head (i.e., an upward vertical offset), as is illustrated byFIG. 19, although there can be exceptions such as in the instance ofdrilling into the side of a hill. If the later is the case, the approachto the over-the-head point may start from an elevated point such as, forexample, on the hill, necessarily above the probe.

Having eliminated the vertical ambiguity, probe 422 senses rotatingmagnetic field 406 in step 464 to produce raw sensor output data. Thesystem uses the sensed field data to determine, in step 466, theposition of the probe/receiver, as outlined above, bearing in mind theone remaining ambiguity in the X,Y plane. This solution, therefore,includes two possible positions of the over-the-head point, on oppositesides of the locator. It should be appreciated that the determination ofthis solution can be physically distributed in a number of ways, all ofwhich are considered to be appropriate. For example, probe 422 of FIG.19 can detect dipole field 406 and transfer the raw sensor data tolocator 400 in an appropriate manner, such as described above. Thelocator then uses the raw data information to establish the positiondetermination. Alternatively, the probe can determine its position,based on the sensed, raw data, and then transmit the positioninformation to the locator. As another alternative, a base station canbe used to receive data from the probe and then pass appropriateinformation along to the locator. The base station can receive rawsensor data, determined position information from probe 422 or somecombination of raw and processed data.

Referring to FIG. 23, along with FIGS. 18, 19 and 22, at least one ofthese possible over-the-head points, shown as a “ball” 452 a in FIG. 23is indicated in step 468. It is noted that this initial display couldplace the “ball” in any one of the quadrants based upon the currentorientation of locator 400, relative to probe 422. The position has beenillustrated in one of the two upper quadrants of a display 450 forpurposes of convenience. It is further noted that locator 400 can beconfigured to arbitrarily select one of the possible OH points or mayalways display that possible OH point which appears in the upper (orlower) display quadrants. Display 450 is diagrammatically illustratedand may readily be provided on locator 400 of FIG. 18 using any suitabledisplay type such as, for example, LCD, plasma and/or LED. Display 450shows “box” 454 approximately at its center and may provide additionalinformation such as, for example, the values of X_(p),Y_(p) and Z_(p).As will be seen, the possible or potential displayed over-the-head pointmay or may not coincide with the actual over-the-head point. Generally,the X axis is arranged to project straight forward when the locator isheld comfortably by its operator. Further, the X axis of displayed 450can be aligned with this direction.

Referring to FIG. 24, display 450 is shown in a modified form, withrespect to FIG. 23, wherein both possible over-the-head points areindicated as 452 a and 452 b. The points are distinguishable by aslightly different outward appearance. One of these points correspondsto the actual over-the-head point. As will be seen below, the operatorcan select and initially use either one of these possible OH points.

Having a suitable display presented, such as is represented, forexample, by FIGS. 23 and 24, in step 470, the operator rotationallyorients locator 400 toward the displayed position of the selected one ofthe possible OH points. Responsive to this rotation, the possible OHpoint of interest will move to one of the upper display quadrants, if itis not already in such position. The operator then moves locator 400 atleast generally toward the selected one of the possible over-the-headpoints 452 a,b. Responsive to this movement, the selected possible OHpoint will move closer to the box at the center of the display, if it isthe actual OH position. In this regard, since the distance change may besmall, and therefore difficult to detect on the screen monitor, theappearance of the “ball” and/or display values can be changed by step470 based on a current change in the value of distance and/or signalstrength. For example, the “ball” can change from a lightly shadedcircle to a solid dot when the distance to the OH location decreases.Similarly, flashing symbols or color changes can also indicate adistance decrease. It should be appreciated that the signal strengthwill increase when the actual OH location is approached.

If the “shadow” OH position is initially selected, as determined by the“ball” moving farther from the box when the locator is moved toward theshadow possible OH point, the locator is rotated by 180 degrees so thatit faces the actual OH point. At the same time, locator 400 reconfiguresdisplay 450 to illustrate the actual OH point in one of the upperdisplay quadrants. Irrespective of whether the actual or shadow OH pointis initially selected, the actual OH point is readily identified by thisprocess.

Having identified the actual OH point, in step 472, the operatorcontinues to move locator 400 toward the actual OH point until thelocator is indicated as being directly overhead. That is, “ball” 452 isin box 454. Again, since actual coordinates of the OH point aredetermined, it may not be necessary to physically move the locator allthe way to the actual OH point.

Locator 400 is particularly advantageous with respect to the accuracy ofthe depth determinations which it produces. In particular, depthaccuracy increases as the overhead point is approached. In view ofequation (48) above, the error of estimating depth using measureddistances R,r can be written as:

$\begin{matrix}{e_{Z_{p}} = {\frac{1}{Z_{p}}\sqrt{{R^{2}e_{R}^{2}} + {r^{2}e_{r}^{2}}}}} & (49)\end{matrix}$

where e_(R),e_(r) are the corresponding distance measurement errors.Clearly, for a given value of depth Z_(p), depth measurement accuracyincreases (i.e., e_(Z) _(p) decreases), as R and r decrease withapproaching the overhead point.

Tilt Correction

The foregoing descriptions are premised upon maintaining a verticalmagnet position or compensating, in some manner, for variations fromvertical. The former can be achieved by either manually leveling thelocator or using a magnet suspension designed to keep the magnetvertically oriented, irrespective of locator tilt, while the latter canbe achieved using a mathematical tilt correction. It is to be understoodthat this tilt compensation technique is applicable to both stationarytransmitters operating at an at least temporarily fixed position at thesurface of the ground as well as portable devices including those whichare hand carried by an operator. The same mathematical tilt correctionmay be applied to both stationary and portable devices.

It is considered that one having ordinary skill in the art may readilyimplement manual leveling or an appropriate magnet suspension, forexample, using a weighted gyroscopic-type gimbal. The mathematical tiltcorrection approach is outlined immediately hereinafter.

Referring to FIG. 25, a level X,Y reference plane 460 isdiagrammatically illustrated in a perspective view. Tilt angles,sometimes referred to as gravitational angles, are defined and measuredwith respect to this plane using a tilt sensor in locator 400. Here, atilt-pitch angle γ_(x) is a rotation about the Y-axis whereas atilt-roll angle γ_(y) is a rotation about the X-axis.

Referring to FIGS. 26 and 27, a tilted Cartesian coordinate system(X′,Y′,Z′) is illustrated that changes orientation with the locator andwhich is associated with the X,Y,Z system by two rotations, one aboutthe X axis (FIG. 27), given by an angular value θ, and another about theY′ axis (FIG. 26), given by an angular value λ. This system coincideswith a level coordinate system (X,Y,Z) when the locator is in a levelposition.

Prior to mathematically correcting for locator tilt, probe coordinatesare determined in tilted coordinates X″,Y″,Z″ employing the analysis ofsensed rotating dipole field data, as given above. Specifically, theover-the-head position is (X_(p)″,Y_(p)″) and vertical probe position isZ_(p)″<0 if the X″,Y″-plane of the tilted locator is above the probe,otherwise Z_(p)″>0.

Still referring to FIGS. 26 and 27, a roll Euler transformation and apitch Euler transformation convert probe coordinates from a tilted to alevel system. The required Euler angles for pitch and roll can bederived from the measured tilt angles using

$\begin{matrix}{\lambda = \gamma_{x}} & (50) \\{\theta = {\arcsin \left( \frac{\sin \; \gamma_{y}}{\cos \; \gamma_{x}} \right)}} & (51)\end{matrix}$

Note that for small tilt angles the Euler roll angle θ is approximatelygiven by the tilt-roll angle γ_(y). Finally, probe coordinates in alevel system follow from

$\begin{matrix}{\begin{Bmatrix}X_{p} \\Y_{p} \\Z_{p}\end{Bmatrix} = {{\begin{bmatrix}1 & 0 & 0 \\0 & {\cos \; \theta} & {\sin \; \theta} \\0 & {{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}{\cos \; \lambda} & 0 & {\sin \; \lambda} \\0 & 1 & 0 \\{{- \sin}\; \lambda} & 0 & {\cos \; \lambda}\end{bmatrix}}\begin{Bmatrix}X_{p}^{''} \\Y_{p}^{''} \\Z_{p}^{''}\end{Bmatrix}}} & (52)\end{matrix}$

Logging Probe Position Data

Referring to FIGS. 28 and 29, logging of drillpath data will now bedescribed. FIG. 28 illustrates a region, generally indicated by thereference number 470, in a diagrammatic plan view in which data loggingis to take place. Region 470 includes a sidewalk 472 adjacent to astreet 474. An intended drill path 476, beneath the street, is shownusing a dashed line. This technique is useful from any convenientreference line such as, for example, an edge or curb 478 of sidewalk472. FIG. 28 also illustrates region 470, but in an elevational view,including locator 400 positioned above curb 478 and probe 422 shown atsome point along drill path 476. A series of reference locations 480 a-eis designated along a length of curb 478. Such reference locations canbe marked and measured employing either standard surveying techniques orusing a global positioning system (GPS). With locator 400 heldimmediately above each of these reference locations as probe 422progresses along drill path 476, a series of corresponding OH points 481a-e is identified in a one-to-one correspondence with reference points480 a-e.

As shown in FIG. 29, Y_(p) and Z_(p) are determined based on theposition of magnet 404 (shown as an intersection in locator 400). FIG.28 illustrates Y_(p), as determined for points 480 a and 481 a. Thevertical offset of the locator above the surface of the ground may becompensated for in any suitable manner such as, for example, pre-mappingthe surface of the ground in the vicinity, as described above. Whileeach of the OH points is shown at a normal angle in relation to curb478, it should be appreciated that this is not a requirement. It isnoted that this procedure is advantageous with respect to the fact thatthe operator is not required to walk to the OH position. In this regard,the present technique benefits from the determination of the actuallocation of the overhead point relative to the locator, as describedabove.

Referring now to FIGS. 30 and 31, a logging procedure will now bedescribed which relies only on the determined over-the-head positions.That is, there is no need to use a GPS or other survey apparatus,although this method assumes that the locator features some mechanismfor orienting the locator in a specified compass direction. One choicewould be to use a magnetometer for detecting compass direction byfiltering out the rotating magnetic field generated by the rotatingmagnet. Another approach would rely on deducing the magnet orientationwith respect to the Earth field by extracting compass direction fromvoltage and current driving the rotation motor for the magnet.

FIG. 30 is a plan view of a region 482 in which this logging operationis to take place, showing locator 400 at a prior over-the-head point 484above a drill path 486. FIG. 31 is an elevational view of region 482showing locator 400 (i.e., magnet 404) positioned at prior OH point 484.Accordingly, probe 422, traveling from left to right in the view of thefigure has already traveled through prior OH point 484 and has reached acurrent OH point 488. Thus, the drill path shown to the right of probe422 (see FIG. 31) is an intended path. Probe position dataX_(p),Y_(p),Z_(p) are recorded while the locator is at prior OH position484. Again, throughout this data logging process the locator shouldalways be pointed in the same compass direction which, in the presentexample, is to the right in the view of these figures. Probe positiondata are determined before moving locator 400 from prior OH point 484 tocurrent OH position 488 in order to locate and log data in an efficientmanner. The current OH position then becomes a prior OH position suchthat the described process is repeated to incrementally log the probepositions across the region of interest. It is noted that data can belogged at arbitrary rod length intervals. Furthermore, rodidentification numbers do not need to be recorded. Drillpath positionsare obtained by adding all previous recorded probe position data, eitherin real time while drilling or after completion of the bore. Once again,this procedure relies on the highly advantageous capability of thissystem to remotely determine the actual coordinates of the OH position.

Another embodiment of locator 400 will now be described which does notprovide a complete set of probe position coordinates but which,nonetheless, should provide very accurate depth determination, forexample, in the presence of rebar.

Data Acquisition and Analysis

Data acquisition, in the context of this embodiment, relies only onmeasured magnitude of flux, but does not require measurement of magnetrotation angles corresponding to flux measurements. Accordingly, fluxmeasurements can be performed over at least one half of a magnetrotation such that these flux measurements provide for determination ofmaximum and minimum values b_(max),b_(min). Such minimum and maximumflux values can be seen in FIG. 21. The measured data can be processedin two ways, denoted as Method a and Method b, as described immediatelyhereinafter.

Method a

From the recorded set of fluxes, maximum and minimum valuesb_(max),b_(min) are extracted. As described with respect to FIG. 20above, a maximum flux is measured when dipole axis 408 points at theover-the-head position or in the opposite direction(ρ=ρ_(OH),ρ=ρ_(OH)+π). A minimum value occurs when ρ=ρ_(OH)±π/2. Thatis, the dipole axis is perpendicular to the direction that is toward theover-the-head position. Introducing this information to equation (42)yields

b _(max) =R ⁻⁴√{square root over (3r ² +R ²)}  (53)

b_(min)=R⁻³  (54)

Hence, the following equations are obtained for the determination ofr,R,Z_(p)

$\begin{matrix}{R = b_{\min}^{{- 1}/3}} & (55) \\{r = {\frac{1}{\sqrt{3}}b_{\min}^{{- 4}/3}\sqrt{b_{\max}^{2} - b_{\min}^{2}}}} & (56) \\{Z_{p} = {\pm \sqrt{R^{2} - r^{2}}}} & (57)\end{matrix}$

Method b

Referring to FIG. 32, a diagrammatic plan view of magnet 404 isprovided, illustrating the use of a rotation angle φ. This approach issimilar to the phase method described above by equations (19) to (23).However, instead of measuring rotation angle φ, angle φ is used from arecorded time t and magnet rotation frequency f based on

φ=2πft  (58)

According to this definition, rotation angle φ=0 at time t=0 when afirst set of fluxes is measured. Angle φ has the value φ₀ when dipoleaxis aligns in the X-direction of the locator coordinate system. Itshould be noted that it is easier to obtain rotation angle φ than tomeasure angle ρ, which would require a measurement of φ₀. Radii r,R anddepth Z_(p) are obtained from a curvefit of the measured square fluxesb²

g=c ₁ cos²( c ₃−φ)+c ₂  (59)

and the following equations.

$\begin{matrix}{R^{2} = \left( \frac{1}{c_{2}} \right)^{1/3}} & (60) \\{r^{2} = \frac{c_{1}R^{8}}{3}} & (61) \\{Z_{p} = {\pm \sqrt{R^{2} - r^{2}}}} & (62)\end{matrix}$

Note that Methods a and b do not provide X_(p),Y_(p) coordinates of theover-the-head position, however, these coordinates are not needed in thecontext of finding the OH point, as described immediately hereinafter.

Locating Procedure

Locating the over-the-head position with this embodiment is somewhatdifferent from that of the aforedescribed embodiment which yields theactual X_(p),Y_(p) coordinates. While the described technique uses theminimum flux b_(min) and distance r from the locator to theover-the-head point, it should be appreciated that any one of thevariables r,R,b_(min),b_(max) or additional dependent variables, derivedfrom these variables, could form the basis of a locating procedure. Thechoice of b_(min) and r does, however, appear to be well-suited to thetask.

Referring to FIG. 33, contours 500 of constant minimum flux on a levelground 502 form concentric circles around an OH point 504. FIG. 33 showsthe flux for a probe depth of 20 feet. Each circular gradient line wouldbe observed by moving locator 400 radially around OH point 504. In thisregard, it is noted that these gradient lines are a construct, formingpart of the locating technique, and do not exist in a temporal sense.When approaching the OH point from a distance of 30 feet, for example,along a path 506, the gradients of minimum flux become increasinglycloser to one another until the locator is moved to within approximately10 feet of the OH point. Closer to OH point 504, flux changes are stillsufficiently large to locate this point with confidence, particularly inconjunction with monitoring distance r to pinpoint this positionexactly.

FIG. 33 is a plot 510 of minimum flux times 10⁵ versus radial distance rfrom OH point 504, further illustrating the suitability of using minimumflux in locating this point. In particular, a relatively sharp gradientand flux intensity is seen from 30 feet out, continuing up to arelatively small distance from the OH point. Accordingly, a peak inminimum flux intensity will be observed upon passing through the OHpoint.

In most situations, the user will follow the drill string in thedirection of an assumed over-the-head position. Frequent sweeping in alldirections allows the user to determine the direction of largest fluxgradient which can readily be tracked to the OH position. For example,locator 400 can display b_(min) flux intensity and/or distance r. If theuser is relying on displayed flux intensity, the user simply moves thelocator in a way which causes a continuously increasing value ofb_(min). In the case of using r, the user simply moves the locator in away which causes a continually decreasing value of r.

Horizontal Magnet Locator

FIG. 34 illustrates another embodiment of a single magnet locatingsystem. Specifically, a locator 520 is shown having a horizontal magnet522. The latter and locator 520 are shown in a plan view such thatmagnet 522 has a horizontal axis of rotation 524 that is coincident withthe Y axis. FIG. 35 is a diagrammatic view, in elevation, showinghorizontal rotating magnet 522 in relation to probe 422 in order tofurther characterize their relationship. It should be appreciated, inthis regard, that a magnet with a horizontal axis of rotation can bemounted in the locator in any number of different ways and alignment ofthe magnet rotational axis with some other horizontal direction mayreadily be accommodated in view of the present disclosure. Dataacquisition, specifically the measurement of fluxes and rotation angles,is nearly identical to that of the vertical magnet locator. Further,data analysis closely follows the procedure that is described in detailabove. Accordingly, these discussions will not be repeated for purposesof brevity. For locator 520 depicted in FIG. 34, probe positioncoordinates are obtained from

X _(p) = r cos( ρ _(p))  (63)

Y _(p) =±√{square root over (R ² − r ²)}  (64)

Z _(p) =− r sin( ρ _(p))  (65)

Here, radii R, r are calculated from the curvefit coefficients of themeasured square fluxes, as described above for the vertical magnetlocator.

Having described a number of embodiments using a single magnet in avertical or horizontal orientation, it should be mentioned that aparticular advantage is shared by these embodiments. In particular, asdescribed above, as the over-the-head point is approached, the accuracywith which depth is determined actually increases.

The locator of the present invention improves drillhead tracking atleast in the following areas. It allows accurate tracking under rebar,due to the very low frequency of the rotating dipole field. Presently,the DCI Eclipse® system (by Digital Control, Inc.) utilizes operatingfrequencies of about 12 kHz and 1.5 kHz, respectively. Notice a magnetrotation frequency of 2 Hz is three orders of magnitude lower than 1.5kHz and is therefore expected to reduce rebar effects significantly. Animproved locating capability is provided since probe position relativeto the locator can be displayed. The locating procedure focuses onfinding the over-the-head position on the ground surface immediatelyabove the probe. For this purpose, the new locator uses a“ball-in-the-box” display and method reminiscent of the Eclipse® displaybut here the “ball” is a display of actual over-the-head coordinates, atechnique which could not be implemented for the Eclipse® system. Inaddition, by varying the frequency of the rotating magnet and analyzingthe sensor data one can extrapolate to zero frequency, thus minimizinginfluences of conducting material as described in U.S. Pat. No.6,285,190 which is commonly owned with the present application and isincorporated herein by reference.

Referring now to FIG. 37, another system, that is produced in accordancewith the present invention, is generally indicated by the referencenumber 600. This system is useful in determining the position of anin-ground object such as, for example, a drillhead or other item thatcan be configured with a receiver or detector 602, with great accuracy.The system employs at least three generators of rotating dipole fieldsthat are indicated as Magnet 1, Magnet 2 and Magnet 3. As is evident inview of the discussions above, each generator produces a rotating dipolefield 603 (shown for Magnet 1) by rotating a dipole axis 604 of eachmagnet about an axis 606 that is typically at least approximately normalto the dipole axis. Each magnet is mounted in a separate housing (notshown). Detector 602 is made up of three flux sensors that may beselected in accordance with the precepts given above. It should beappreciated that rotating fields can either be generated by magnets, asshown, which rotate about a single axis or by a pair of antennasinducing time-varying fluxes. Accordingly, the following descriptionuses the term “magnet” to denote either an actual magnet or anappropriate pair of antennas.

Magnets 1-3 are generally placed above ground, but occasionally anapplication could require the placement of rotating magnets below theground surface. In the present example, the XY plane represents thesurface of the ground. Magnets 1 and 2 are above the surface of theground while Magnet 3 is below the surface of the ground. As indicatedin the figure, rotation axis orientation angles are arbitrary and neednot be measured. In order to minimize interference effects, the magnetcan be rotated slowly at low frequencies (revolutions per second) thatrange from a fraction of a Hertz to 500 Hz or more. Differentfrequencies are required to distinguish fluxes induced by the magnets atthe location of the detector. Alternatively, the system can be designedwith different operating time-slots assigned to each magnet, in whichcase all magnets could rotate at the same frequency.

As described above, each magnet produces a rotating three-dimensionalmagnetic dipole field having an axis of symmetry that is normal to therotation axis. The rotating dipole induces a time-varying flux atdetector 602 that is measured using three essentially orthogonal fluxsensors. Either magnetometers or coils can be used as flux sensingdevices, as described above, so long as a total flux strength isdeterminable in three dimensions. Total flux is calculated as themagnitude of the vector sum of the three orthogonal flux components. Theposition identifying method that is used in conjunction with thisembodiment does not require the measurement of rotation angles of themagnets, as will be seen.

During magnet rotation, the time-varying flux, responsive to eachrotating magnet, generally displays maxima and minima. It is recognizedthat a distance R_(i) between the center of the i-th magnet and detector602 can be obtained based on the use of the minima, maxima, average orsome other suitable flux characteristic that is repeatably ascertainablewith revolution of the magnet. In the instance of using the minima, aminimum value of flux b_(min) _(i) , observed with respect to rotationof one of the magnets, is applied in the formula

R _(i) =b _(min) _(i) ^(−1/3)  (66)

It is recognized that the flux has the same minimum value b_(min) on thesurface of a sphere of radius R_(i) with the i-th magnet at its center.Therefore, the position of detector 603 can be determined, in part, as apoint of intersection of the three spheres enclosing the magnets. Inorder to make this initial determination, the values required to beknown include (i) the positions of the magnets, which can be establishedin a suitable coordinate system, and (ii) a total minimum fluxmeasurement that is induced by each magnet. The coordinate system can beestablished in any suitable manner. For example, one of the magnets maydefine the origin of the coordinate system. The coordinate system axescan be oriented in any suitable manner such as, for example, by beingdefined with respect to a magnet that is at the origin of the coordinatesystem or by using the points of the magnetic compass. Any suitablereference system may be utilized and the descriptions provided hereinare not intended to have any limiting effect with respect to thiscoordinate system.

Assuming the position coordinates of the i-th magnet, denoted by (X_(m)_(i) ,Y_(m) _(i) ,Z_(m) _(i) ), are known, the equation of the i-thsphere is written as

f _(i) =R _(i) ²−(X _(d) −X _(m) _(i) )²−(Y _(d) −Y _(m) _(i) )²−(Z _(d)−Z _(m) _(i) )²=0  (67)

which includes detector 602 position coordinates (X_(d),Y_(d),Z_(d)) asunknowns.

Equation (66) represents a set of i equations (i=1, 2, 3, in the presentexample) which can be solved for its three unknowns using standardnumerical techniques. One suitable technique is unconstrainedoptimization performed with the so-called SIMPLEX method. The latterrequires definition of a function F that needs to be minimized. Aconvenient choice is

F=w ₁ f ₁ ² +w ₂ f ₂ ² +w ₃ f ₃ ² =F _(min)  (68)

Here the symbols w_(i) (i=1, 2, 3) represent arbitrarily chosenweighting functions. Note w_(i)>0 to satisfy each sphere equation (2).In one implementation, set w_(i)=1, but functions like the following canbe selected:

$\begin{matrix}{w_{i} = \frac{const}{R_{i}}} & (69)\end{matrix}$

or some variation of it to account for the decrease of measurementaccuracy with increasing distance R_(i).

One value of the SIMPLEX method resides in its exclusive use of functionevaluation and avoidance of derivatives. One could, of course, employother standard techniques such as a Newton or a nonlinear least squaremethod that use derivatives.

Note that equations (66) are nonlinear and may be solved by iterationstarting from an initial solution estimate. In general, there are atleast two valid solutions for detector position, so that an initialestimate can be selected with the intent of finding the solution thatrepresents the actual detector position. Any suitable additionalinformation may be utilized as input to identify the actual detectorposition, among the possible positions. Often, such suitable additionalinformation is already known. For example, a last known detectorposition may be used as an estimate for the new solution. Alternatively,during drilling in which the detector is moved by a drill string,particularly one including drill pipe sections, an extrapolation can bemade from the last known position based on extension of the drill stringand, if measured, known pitch and yaw to obtain a better initialestimate. Pitch and yaw can be measured at the drill head andtransmitted to the surface for use by a suitable transmitter ortransmitted to the drill string using a wire-in-pipe arrangement such asdescribed in above incorporated U.S. Pat. No. 6,223,826. In the instanceof wireless transmission, the drill head of FIG. 15, described above,may be employed.

Finally, any number of magnets may be added to the system, requiringonly a minor modification of the tracking method. If tracking isperformed with the SIMPLEX method a term w_(i)f_(i) ² must be added toequation (67) for each magnet added to the system. No other modificationof the tracking method is needed. In view of the foregoing descriptions,it is considered that one of ordinary skill in the art is capable ofapplying a suitable numerical technique for purposes of determining thedetector position and for selecting appropriate supplemental informationto resolve multivalued parameters based on a particular implementation.

Although each of the aforedescribed embodiments have been illustratedwith various components having particular respective orientations, itshould be understood that the present invention may take on a variety ofspecific configurations with the various components being located in awide variety of positions and mutual orientations and still remainwithin the spirit and scope of the present invention. For example, areceiver that is described as being housed in a boring tool may often beused in a variety of alternative applications such as, for instance,within a sonde that is designed to transit through a concealed utilityline. Such a utility may be concealed, for example, by the ground orcontained within a wall or floor. Furthermore, suitable equivalents maybe used in place of or in addition to the various components, thefunction and use of such substitute or additional components being heldto be familiar to those skilled in the art and are therefore regarded asfalling within the scope of the present invention. Therefore, thepresent examples are to be considered as illustrative and notrestrictive, and the invention is not to be limited to the details givenherein, but may be modified in any number of alternative ways.

1. In a system including a boring tool that is movable underground usinga drill string which extends from the boring tool to a drill rig thatoperates at the surface of the ground, a method comprising: configuringa transmitter for above ground use and for rotating at least two staticmagnetic fields that are produced by a first magnet and a second magnetrotating about a first axis and a second, different axis, respectively,in a way which produces a first rotating magnetic dipole field and asecond rotating magnetic dipole field such that the first and secondrotating dipole fields are distinguishable, one from the other; using areceiver that is provided as part of said boring tool, at leastperiodically sensing said first and second rotating magnetic dipolefields, to produce a receiver output responsive thereto; and monitoringa positional relationship between the transmitter and the boring tool byusing at least the receiver output to establish an actual position of anoverhead point that is directly above the receiver in a laterallyspaced-apart relationship from the transmitter.
 2. The method of claim 1including displaying the actual position of the overhead point at apredetermined aboveground location.
 3. The method of claim 1 includingproviding a display as part of said transmitter and displaying thepositional relationship on said display to show the actual position ofthe overhead point in relation to a current position and orientation ofthe transmitter.
 4. In a system including a boring tool that is movableunderground using a drill string which extends from the boring tool to adrill rig that operates at the surface of the ground, an apparatuscomprising: a transmitter, for aboveground use, and configured forrotating at least two static magnetic fields that are produced by afirst magnet and a second magnet rotating about a first axis and asecond, different axis, respectively, in a way which produces a firstrotating magnetic dipole field and a second rotating magnetic dipolefield such that the first and second rotating dipole fields aredistinguishable, one from the other; a receiver that is supported insaid boring tool for at least periodically sensing said first and secondrotating magnetic dipole fields, to produce a receiver output responsivethereto; and a processing arrangement for monitoring a positionalrelationship between the transmitter and the boring tool by using atleast the receiver output to establish an actual position of an overheadpoint that is directly above the receiver in a laterally spaced-apartrelationship from the transmitter.
 5. The apparatus of claim 4 includingproviding a display as part of said transmitter and displaying thepositional relationship on said display to show the actual position ofthe overhead point in relation to a current position and orientation ofthe transmitter.
 6. In a system including a boring tool that is movableunderground using a drill string which extends from the boring tool to adrill rig that operates at the surface of the ground, a methodcomprising: configuring a transmitter, located aboveground, for rotatingat least two static magnetic fields that are produced by a first magnetand a second magnet rotating about a first axis and a second, differentaxis, respectively, in a way which produces a first rotating magneticdipole field and a second rotating magnetic dipole field such that thefirst and second rotating dipole fields are distinguishable, one fromthe other; using a receiver that is provided as part of said boringtool, at least periodically sensing said first and second rotatingmagnetic dipole fields, to produce a first set of receiver outputs bymeasuring a first plurality of total flux intensities, in threedimensions, associated with the first rotating magnetic dipole as thefirst magnet rotates through a first plurality of rotation angles whichoccur over at least one-half of a revolution of the first magnet suchthat each one of the first plurality of total flux intensitiescorresponds one-for-one with each one of said first plurality ofrotation angles and to produce a second set of receiver outputs bymeasuring a second plurality of total flux intensities, in threedimensions, associated with the second rotating magnetic dipole as thesecond magnet rotates through a second plurality of rotation angleswhich occur over at least one-half of a revolution of the second magnetsuch that each one of the second plurality of total flux intensitiescorresponds one-for-one with each one of said second plurality ofrotation angles; and monitoring a positional relationship between theboring tool and the transmitter at least by using the first set ofreceiver outputs and the second set of receiver outputs associated withthe first plurality of rotation angles and the second plurality ofrotation angles, respectively, to establish a position of the receiverin relation to a current position and orientation of the transmitter. 7.The method of claim 6 wherein the boring tool travels in a knownelevational relationship with respect to said transmitter and whereinsaid positional relationship is characterized by a set of parameterssuch that a determination of said positional relationship, based solelyon said first set of receiver outputs and said first plurality ofrotation angles produces multiple values for at least some of saidparameters and wherein said second set of receiver outputs is used inconjunction with the second plurality of rotation angles and the knownelevational relationship to resolve said multiple values.
 8. The methodof claim 7 wherein said second set of receiver outputs is at least usedto determine a left/right direction of the receiver in relation to thecurrent position and orientation of the transmitter.
 9. The method ofclaim 6 wherein monitoring the positional relationship includes (i)transferring the first and second sets of receiver outputs to thetransmitter in a predetermined way, (ii) measuring said first and secondplurality of rotation angles at said transmitter, and (iii) providing aprocessing arrangement, which forms part of said transmitter, for usingthe first and second sets of receiver outputs in conjunction with saidfirst and second pluralities of rotation angles, as measured at thetransmitter, to establish said positional relationship.
 10. The methodof claim 6 wherein said first and second rotating magnets are rotatedabout first and second axes, respectively, and measuring includesarranging a first encoder and a second encoder for rotation with each ofthe first and second axes to produce first and second encoder outputsfor use in establishing the first and second pluralities of rotationangles and monitoring includes correlating the first and second encoderoutputs with each one of said first and second pluralities of total fluxintensities for each of the first and second rotating magnets.
 11. Themethod of claim 10 including transferring said first and second encoderoutputs and said first and second plurality of total flux intensities toa predetermined location, prior to said correlating and, thereafter,performing said correlating at the predetermined location.
 12. Themethod of claim 10 including transferring the first and second encoderoutputs to said boring tool such that said correlating is performed atthe boring tool.
 13. The method of claim 10 including transferring saidfirst and second plurality of total flux intensities to the transmitterfor correlation with the first and second pluralities of rotation anglesby the transmitter.
 14. The method of claim 6 including using said firstplurality of total flux intensities and said first plurality of rotationangles to determine (i) a total distance, R, between the portable deviceand the receiver and (ii) a projected distance, r, in a plane that isdefined to include a center point of the first magnet and a center pointof the receiver wherein the axis of rotation of the first magnet is atleast approximately horizontally oriented.
 15. The method of claim 6wherein determining total distance, R, and horizontal distance, r,includes curvefitting said first plurality of total flux intensities atsaid first plurality of rotation angles using${f = {{c_{1}{\cos^{2}\left( {c_{3} - \rho} \right)}} + c_{2}}},{R^{2} = \left( \frac{1}{c_{2}} \right)^{1/3}},{and}$$r^{2} = \frac{c_{1}R^{8}}{3}$ where c₁, c₂ and c₃ are constants and ρis the rotation angle of the first magnet for any given total firstmagnet flux measurement.
 16. The method of claim 15 wherein c₃ is equalto a specific rotation angle ρ_(r) at which a dipole axis of the firstrotating magnetic field is at least approximately oriented toward saidreceiver in said plane and usingX _(r) =r cos(ρ_(r)),Y _(r) =r sin(ρ_(r)), andZ _(r) =√{square root over (R ² −r ²)}, to determine a plurality ofpotential positions of the receiver relative to the portable device,where X_(p),Y_(p) and Z_(p) are multi-valued potential coordinates ofthe receiver in relation to the portable device.
 17. In a systemincluding a boring tool that is movable underground using a drill stringwhich extends from the boring tool to a drill rig that operates at thesurface of the ground, an apparatus comprising: a transmitter configuredfor use aboveground and for rotating at least two static magnetic fieldsthat are produced by a first magnet and a second magnet rotating about afirst axis and a second, different axis, respectively, in a way whichproduces a first rotating magnetic dipole field and a second rotatingmagnetic dipole field such that the first and second rotating dipolefields are distinguishable, one from the other; a receiver, that issupported in said boring tool, for at least periodically sensing saidfirst and second rotating magnetic dipole fields, to produce a first setof receiver outputs by measuring a first plurality of total fluxintensities, in three dimensions, associated with the first rotatingmagnetic dipole as the first magnet rotates through a first plurality ofrotation angles which occur over at least one-half of a revolution ofthe first magnet such that each one of the first plurality of total fluxintensities corresponds one-for-one with each one of said firstplurality of rotation angles and to produce a second set of receiveroutputs by measuring a second plurality of total flux intensities, inthree dimensions, associated with the second rotating magnetic dipole asthe second magnet rotates through a second plurality of rotation angleswhich occur over at least one-half of a revolution of the second magnetsuch that each one of the second plurality of total flux intensitiescorresponds one-for-one with each one of said second plurality ofrotation angles; and a processing arrangement for monitoring apositional relationship between the receiver in the boring tool and thetransmitter by using at least the first set of receiver outputs and thesecond set of receiver outputs associated with the first plurality ofrotation angles and the second plurality of rotation angles,respectively, to establish a position of the receiver in relation to acurrent position and orientation of the transmitter.
 18. The apparatusof claim 17 wherein the boring tool travels in a known elevationalrelationship with respect to said transmitter and wherein saidpositional relationship is characterized by a set of parameters suchthat a determination of said positional relationship, based solely onsaid first set of receiver outputs and said first plurality of rotationangles produces multiple values for at least some of said parameters andwherein said processing arrangement is configured for using said secondset of receiver outputs in conjunction with the second plurality ofrotation angles and the known elevational relationship to resolve saidmultiple values.
 19. The apparatus of claim 18 wherein said processingarrangement uses said second set of receiver outputs at least todetermine a left/right direction of the receiver in relation to thecurrent position and orientation of the portable device.
 20. Theapparatus of claim 17 wherein said processing arrangement forms part ofthe transmitter and said receiver is configured for transferring thefirst and second sets of receiver outputs to the portable device in apredetermined way and said transmitter is configured for measuring eachof the first and second pluralities of rotation angles for use by theprocessing arrangement.
 21. The apparatus of claim 17 wherein said firstand second rotating magnets are rotated about first and second axes,respectively, and said transmitter includes a first encoder and a secondencoder for rotation with each of the first and second axes to producefirst and second encoder outputs for use in establishing the first andsecond pluralities of rotation angles and said processing arrangement isconfigured for correlating the first and second encoder outputs witheach one of said first and second pluralities of total flux intensitiesfor each of the first and second rotating magnets.
 22. The apparatus ofclaim 21 wherein said transmitter and said receiver are cooperativelyconfigured for transferring said first and second encoder outputs andsaid first and second plurality of total flux intensities to apredetermined location of said processing arrangement, prior to saidcorrelating and, thereafter, said processing arrangement performs saidcorrelating at the predetermined location.
 23. The apparatus of claim 21wherein said transmitter and said receiver cooperate to transfer thefirst and second encoder outputs to said boring tool and said processingarrangement is located at the boring tool such that said correlating isperformed 21 104 wherein said transmitter and said receiver cooperate totransfer said first and second plurality of total flux intensities tothe transmitter and said processing arrangement forms part of thetransmitter for correlating the first and second plurality of total fluxintensities with the first and second pluralities of rotation angles atthe transmitter.
 25. The apparatus of claim 21 wherein said processingarrangement is configured for using said first plurality of total fluxintensities and said first plurality of rotation angles to determine (i)a total distance, R, between the portable device and the receiver and(ii) a projected distance, r, in a plane that is defined to include acenter point of the first magnet and a center point of the receiverwherein the axis of rotation of the first magnet is at leastapproximately horizontally oriented.
 26. The apparatus of claim 25wherein said processing arrangement determines total distance, R, andhorizontal distance, r, by curvefitting said first plurality of totalflux intensities at said first plurality of rotation angles using${f = {{c_{1}{\cos^{2}\left( {c_{3} - \rho} \right)}} + c_{2}}},{R^{2} = \left( \frac{1}{c_{2}} \right)^{1/3}},{and}$$r^{2} = \frac{c_{1}R^{8}}{3}$ where c₁, c₂ and c₃ are constants and ρis the rotation angle of the first magnet for any given total firstmagnet flux measurement.
 27. The apparatus of claim 26 wherein c₃ isequal to a specific rotation angle ρ_(r) at which a dipole axis of thefirst rotating magnetic field is at least approximately oriented towardsaid receiver in said plane and said processing arrangement isconfigured for usingX _(r) =r cos(ρ_(r)),Y _(r) =r sin(ρ_(r)), andZ _(r) =√{square root over (R ² −r ²)}, to determine a plurality ofpotential positions of the receiver relative to the portable device,where X_(p),Y_(p) and Z_(p) are multi-valued potential coordinates ofthe receiver in relation to the portable device.